{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Problem definition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Given an undirected graph, ﬁnd the largest subset of vertices in which no two are connected by an edge.\n",
    "\n",
    "energy function: $$H=H_{A}+H_{B}$$\n",
    "where\n",
    "$$H_{A}=A \\sum_{i j \\in E} x_{i} x_{j}$$\n",
    "and\n",
    "$$H_{B}=-B \\sum_{i} x_{i}$$\n",
    "\n",
    "$H_A$ is constraint violation and $H_B$ is cost. Here $x_{i}\\in\\{0,1\\}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# import packages"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cuda\n"
     ]
    }
   ],
   "source": [
    "import pickle\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import networkx as nx\n",
    "import torch\n",
    "import torch.nn as nn\n",
    "from torch.nn.parameter import Parameter\n",
    "from torch.nn.functional import gumbel_softmax\n",
    "\n",
    "# np.random.seed(2050)\n",
    "# torch.manual_seed(2050)\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "use_cuda = torch.cuda.is_available()\n",
    "device = torch.device(\"cuda\" if use_cuda else \"cpu\")\n",
    "print(device)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "# Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "def load_data(path):\n",
    "    with open(path, 'rb') as f:\n",
    "        data = pickle.load(f)\n",
    "    G = nx.from_dict_of_lists(data)\n",
    "    return G\n",
    "\n",
    "# def load_graph(filename):\n",
    "#     G = nx.Graph() # undirected graphs\n",
    "#     for line in open(filename):\n",
    "#         strlist = line.split(',')\n",
    "#         n1 = int(strlist[0])\n",
    "#         n2 = int(strlist[1])\n",
    "#         G.add_edges_from([(n1, n2)])\n",
    "#     return G\n",
    "\n",
    "\n",
    "def train(G, init_tau=10, final_tau=1, hard=False, \n",
    "          drop_temp=True, lr=1e-1, eta=1, max_iters=5000):\n",
    "    \n",
    "    n=G.number_of_nodes()\n",
    "    A = nx.adjacency_matrix(G)\n",
    "    A = torch.from_numpy(A.todense())\n",
    "    A = A.type(torch.float32)\n",
    "    \n",
    "    # set parameters\n",
    "    if use_cuda:\n",
    "        A = A.cuda()\n",
    "        x = torch.randn(n, 1, device='cuda')*1e-5\n",
    "        x.requires_grad = True\n",
    "    else:\n",
    "        x = torch.randn(n, 1, requires_grad=True)*1e-5\n",
    "\n",
    "    # set optimizer\n",
    "    optimizer = torch.optim.SGD([x], lr=lr)\n",
    "#     optimizer = torch.optim.Adam([x], lr=lr)\n",
    "\n",
    "    tau=init_tau\n",
    "    minus_temp = (init_tau - final_tau) / max_iters\n",
    "    cost_arr = []\n",
    "    \n",
    "    for iters in range(max_iters):\n",
    "        optimizer.zero_grad()\n",
    "        if use_cuda:\n",
    "            probs = torch.empty(n, 2, device='cuda')\n",
    "        else:\n",
    "            probs = torch.empty(n, 2)\n",
    "        p = torch.sigmoid(x)\n",
    "        probs[:, 0] = p.squeeze()\n",
    "        probs[:, -1] = 1-probs[:, 0]\n",
    "        logits = torch.log(probs+1e-10)  # [n,2]\n",
    "        s = gumbel_softmax(logits, tau=tau, hard=hard)  # [n,2]\n",
    "        s = s[:, 0]\n",
    "        s = torch.unsqueeze(s, 1)\n",
    "        cost = -torch.sum(s)\n",
    "        constraint = s.t()@A@s\n",
    "        loss = cost+eta*constraint\n",
    "        loss.backward()\n",
    "        optimizer.step()\n",
    "        if drop_temp:\n",
    "            tau -= minus_temp\n",
    "        \n",
    "        with torch.no_grad():\n",
    "            s=gumbel_softmax(logits,tau=tau,hard=True) #[n,2]\n",
    "            s=s[:,0]\n",
    "            s=torch.unsqueeze(s,1)\n",
    "            constraint=s.t()@A@s\n",
    "            if constraint == 0:\n",
    "                cost=-torch.sum(s)\n",
    "                cost_arr.append(cost.cpu())\n",
    "    print(len(cost_arr))\n",
    "    return cost_arr"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "# Experiments on real-world networks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "## Cora"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2708 5278\n"
     ]
    }
   ],
   "source": [
    "# G=load_graph('./data/cora.edges')\n",
    "G=load_data('./data/ind.cora.graph')\n",
    "print(G.number_of_nodes(), G.number_of_edges())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "can't convert np.ndarray of type numpy.int32. The only supported types are: float64, float32, float16, int64, int32, int16, int8, uint8, and bool.",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-4-880d36be367a>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      1\u001b[0m \u001b[1;31m# cost=train(G, lr=1, max_iters=20000)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 2\u001b[1;33m \u001b[0mcost\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mtrain\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mG\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0minit_tau\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mhard\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mTrue\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0mdrop_temp\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;32mFalse\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mlr\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m1e-2\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0meta\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m15\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mmax_iters\u001b[0m\u001b[1;33m=\u001b[0m\u001b[1;36m20000\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      3\u001b[0m \u001b[0mprint\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mmin\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mcost\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;32m<ipython-input-2-3f79c8648d4e>\u001b[0m in \u001b[0;36mtrain\u001b[1;34m(G, init_tau, final_tau, hard, drop_temp, lr, eta, max_iters)\u001b[0m\n\u001b[0;32m     20\u001b[0m     \u001b[0mn\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0mG\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mnumber_of_nodes\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     21\u001b[0m     \u001b[0mA\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mnx\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0madjacency_matrix\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mG\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 22\u001b[1;33m     \u001b[0mA\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mtorch\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfrom_numpy\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mA\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtodense\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     23\u001b[0m     \u001b[0mA\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0mA\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mtype\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0mtorch\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mfloat32\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     24\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mTypeError\u001b[0m: can't convert np.ndarray of type numpy.int32. The only supported types are: float64, float32, float16, int64, int32, int16, int8, uint8, and bool."
     ]
    }
   ],
   "source": [
    "# cost=train(G, lr=1, max_iters=20000)\n",
    "cost=train(G, init_tau=1,hard=True,drop_temp=False, lr=1e-2, eta=15, max_iters=20000)\n",
    "print(min(cost))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "## Citeseer"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3264 4536\n"
     ]
    }
   ],
   "source": [
    "G=load_graph('./data/citeseer.edges')\n",
    "print(G.number_of_nodes(), G.number_of_edges())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1939\n",
      "tensor(-5.)\n"
     ]
    }
   ],
   "source": [
    "G = nx.grid_2d_graph(3, 3)\n",
    "cost=train(G, init_tau=1,hard=True,drop_temp=False, lr=1e-2, eta=15, max_iters=2000)\n",
    "print(min(cost))\n",
    "# G = nx.grid"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "# Gumbel-softmax optimization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "## N parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 1min 9s, sys: 1.18 s, total: 1min 10s\n",
      "Wall time: 1min 10s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "# G = load_graph('./data/cora.edges')\n",
    "G = nx.grid_2d_graph(10, 10, periodic=False)\n",
    "n = G.number_of_nodes()\n",
    "max_iters = 40000\n",
    "lr = 1e-2\n",
    "tau = 0.5\n",
    "eta = 15\n",
    "\n",
    "torch.manual_seed(1)\n",
    "\n",
    "A = nx.adjacency_matrix(G)\n",
    "A = torch.from_numpy(A.todense())\n",
    "A = A.type(torch.float32)\n",
    "\n",
    "# set parameters\n",
    "if use_cuda:\n",
    "    A = A.cuda()\n",
    "    x = torch.randn(n, 1, device='cuda')*1e-5\n",
    "    x.requires_grad = True\n",
    "else:\n",
    "    x = torch.randn(n, 1, requires_grad=True)*1e-5\n",
    "\n",
    "# set optimizer\n",
    "optimizer = torch.optim.SGD([x], lr=lr)\n",
    "\n",
    "# log\n",
    "cost_arr = []\n",
    "constrain_arr = []\n",
    "\n",
    "for i in range(max_iters):\n",
    "    optimizer.zero_grad()\n",
    "    if use_cuda:\n",
    "        probs = torch.empty(n, 2, device='cuda')\n",
    "    else:\n",
    "        probs = torch.empty(n, 2)\n",
    "    p = torch.sigmoid(x)\n",
    "    probs[:, 0] = p.squeeze()\n",
    "    probs[:, -1] = 1-probs[:, 0]\n",
    "    logits = torch.log(probs+1e-10)  # [n,2]\n",
    "    s = gumbel_softmax(logits, tau=tau, hard=True)  # [n,2]\n",
    "    s = s[:, 0]\n",
    "#     print(s.size())\n",
    "    s = torch.unsqueeze(s, 1)\n",
    "#     print(s.size())\n",
    "    cost = -torch.sum(s)\n",
    "    constraint = s.t()@A@s\n",
    "\n",
    "    loss = cost+eta*constraint\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    with torch.no_grad():\n",
    "#         s=gumbel_softmax(logits,tau=tau,hard=True) #[n,2]\n",
    "#         s=s[:,0]\n",
    "#     #     print(s.size())\n",
    "#         s=torch.unsqueeze(s,1)\n",
    "#     #     print(s.size())\n",
    "#         cost=-torch.sum(s)\n",
    "#         constraint=s.t()@A@s\n",
    "        if constraint == 0:\n",
    "            cost_arr.append(cost.cpu())\n",
    "#         constrain_arr.append(constraint.cpu())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f4e913df518>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 4))\n",
    "plt.subplot(121)\n",
    "plt.plot(cost_arr, label='cost')\n",
    "plt.subplot(122)\n",
    "plt.plot(constrain_arr, label='constrain')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "## k * N parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 7.33 s, sys: 325 ms, total: 7.66 s\n",
      "Wall time: 7.95 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "G = load_graph('./data/cora.edges')\n",
    "n = G.number_of_nodes()\n",
    "max_iters = 5000\n",
    "lr = 1e-2\n",
    "tau = 1\n",
    "eta = 5\n",
    "\n",
    "torch.manual_seed(1)\n",
    "\n",
    "A = nx.adjacency_matrix(G)\n",
    "A = torch.from_numpy(A.todense())\n",
    "A = A.type(torch.float32)\n",
    "\n",
    "# set parameters\n",
    "if use_cuda:\n",
    "    A = A.cuda()\n",
    "    x=torch.rand(5,1,device='cuda')\n",
    "    W=torch.randn(n,5,device='cuda')*1e-5\n",
    "#     x = torch.randn(n, 1, device='cuda')*1e-5\n",
    "    W.requires_grad = True\n",
    "else:\n",
    "    x = torch.randn(5, 1)\n",
    "    W = torch.randn(n,1,requires_grad=True)\n",
    "\n",
    "# set optimizer\n",
    "optimizer = torch.optim.RMSprop([W], lr=lr)\n",
    "\n",
    "# log\n",
    "cost_arr = []\n",
    "constrain_arr = []\n",
    "\n",
    "for i in range(max_iters):\n",
    "    optimizer.zero_grad()\n",
    "    if use_cuda:\n",
    "        probs = torch.empty(n, 2, device='cuda')\n",
    "    else:\n",
    "        probs = torch.empty(n, 2)\n",
    "    p = torch.sigmoid(W@x)\n",
    "    probs[:, 0] = p.squeeze()\n",
    "    probs[:, -1] = 1-probs[:, 0]\n",
    "    logits = torch.log(probs+1e-10)  # [n,2]\n",
    "    s = gumbel_softmax(logits, tau=tau, hard=True)  # [n,2]\n",
    "    s = s[:, 0]\n",
    "#     print(s.size())\n",
    "    s = torch.unsqueeze(s, 1)\n",
    "#     print(s.size())\n",
    "    cost = -torch.sum(s)\n",
    "    constraint = s.t()@A@s\n",
    "\n",
    "    loss = cost+eta*constraint\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    with torch.no_grad():\n",
    "        #         s=gumbel_softmax(logits,tau=tau,hard=True) #[n,2]\n",
    "        #         s=s[:,0]\n",
    "        #     #     print(s.size())\n",
    "        #         s=torch.unsqueeze(s,1)\n",
    "        #     #     print(s.size())\n",
    "        #         cost=-torch.sum(s)\n",
    "        #         constraint=s.t()@A@s\n",
    "\n",
    "        cost_arr.append(cost.cpu())\n",
    "        constrain_arr.append(constraint.cpu())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f0c6f4c36a0>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 4))\n",
    "plt.subplot(121)\n",
    "plt.plot(cost_arr, label='cost')\n",
    "plt.subplot(122)\n",
    "plt.plot(constrain_arr, label='constrain')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[tensor(-1430.),\n",
       " tensor(-1430.),\n",
       " tensor(-1430.),\n",
       " tensor(-1430.),\n",
       " tensor(-1430.),\n",
       " tensor(-1430.),\n",
       " tensor(-1430.),\n",
       " tensor(-1430.),\n",
       " tensor(-1430.),\n",
       " tensor(-1430.),\n",
       " tensor(-1430.),\n",
       " tensor(-1430.),\n",
       " tensor(-1430.),\n",
       " tensor(-1430.),\n",
       " tensor(-1430.),\n",
       " tensor(-1430.),\n",
       " tensor(-1430.),\n",
       " tensor(-1430.),\n",
       " tensor(-1430.)]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cost_arr[-20:-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true,
    "hidden": true
   },
   "source": [
    "## test on disjoint graphs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = nx.Graph()\n",
    "\n",
    "G.add_edges_from([(0,1),(1,3),(1,2),(2,3),(3,5),(3,4),(2,6),(2,4),(4,5),(5,6),(3,7),(4,7),(6,7),(4,6)])\n",
    "\n",
    "nx.draw_networkx(G)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "CPU times: user 2.46 s, sys: 127 ms, total: 2.59 s\n",
      "Wall time: 2.59 s\n"
     ]
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "# G = createGraph('./data/cora.edges')\n",
    "# G = nx.Graph()\n",
    "\n",
    "# G.add_edges_from([(0,1),(1,2),(3,4),(4,5)])\n",
    "\n",
    "n = G.number_of_nodes()\n",
    "max_iters = 2000\n",
    "lr = 1e-1\n",
    "tau = 1\n",
    "eta = 5\n",
    "\n",
    "# torch.manual_seed(1)\n",
    "A = nx.adjacency_matrix(G)\n",
    "A = torch.from_numpy(A.todense())\n",
    "A = A.type(torch.float32)\n",
    "\n",
    "# set parameters\n",
    "if use_cuda:\n",
    "    A = A.cuda()\n",
    "    x = torch.randn(n, 1, device='cuda')*1e-5\n",
    "    x.requires_grad = True\n",
    "else:\n",
    "    x = torch.randn(n, 1, requires_grad=True)*1e-5\n",
    "\n",
    "# set optimizer\n",
    "optimizer = torch.optim.SGD([x], lr=lr)\n",
    "\n",
    "# log\n",
    "cost_arr = []\n",
    "constrain_arr = []\n",
    "\n",
    "for i in range(max_iters):\n",
    "    optimizer.zero_grad()\n",
    "    if use_cuda:\n",
    "        probs = torch.empty(n, 2, device='cuda')\n",
    "    else:\n",
    "        probs = torch.empty(n, 2)\n",
    "    p = torch.sigmoid(x)\n",
    "    probs[:, 0] = p.squeeze()\n",
    "    probs[:, -1] = 1-probs[:, 0]\n",
    "    logits = torch.log(probs+1e-10)  # [n,2]\n",
    "    s = gumbel_softmax(logits, tau=tau, hard=True)  # [n,2]\n",
    "    s = s[:, 0]\n",
    "#     print(s.size())\n",
    "    s = torch.unsqueeze(s, 1)\n",
    "#     print(s.size())\n",
    "    cost = -torch.sum(s)\n",
    "    constraint = s.t()@A@s\n",
    "\n",
    "    loss = cost+eta*constraint\n",
    "    loss.backward()\n",
    "    optimizer.step()\n",
    "    with torch.no_grad():\n",
    "        #         s=gumbel_softmax(logits,tau=tau,hard=True) #[n,2]\n",
    "        #         s=s[:,0]\n",
    "        #     #     print(s.size())\n",
    "        #         s=torch.unsqueeze(s,1)\n",
    "        #     #     print(s.size())\n",
    "        #         cost=-torch.sum(s)\n",
    "        #         constraint=s.t()@A@s\n",
    "\n",
    "        cost_arr.append(cost.cpu())\n",
    "        constrain_arr.append(constraint.cpu())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f0c6ef028d0>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 4))\n",
    "plt.subplot(121)\n",
    "plt.plot(cost_arr, label='cost')\n",
    "plt.subplot(122)\n",
    "plt.plot(constrain_arr, label='constrain')\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[1.],\n",
       "        [0.],\n",
       "        [0.],\n",
       "        [1.],\n",
       "        [1.],\n",
       "        [0.],\n",
       "        [0.],\n",
       "        [1.]], device='cuda:0', grad_fn=<UnsqueezeBackward0>)"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "with torch.no_grad():\n",
    "    p=torch.sigmoid(x)\n",
    "\n",
    "p[p>0.5]=1\n",
    "p[p<0.5]=0\n",
    "\n",
    "p=p.cpu().numpy().astype(np.int)\n",
    "p.reshape(-1,)\n",
    "\n",
    "partition = {}\n",
    "for idx, n in enumerate(G.nodes()):\n",
    "    partition[n] = int(p[idx])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pos=nx.layout.spring_layout(G)\n",
    "plt.figure(figsize=(6,6))\n",
    "colors=[\"r\",'m','b',\"g\",]\n",
    "for com in set(partition.values()) :\n",
    "    list_nodes = [nodes for nodes in partition.keys()\n",
    "                                if partition[nodes] == com]\n",
    "    nx.draw_networkx_nodes(G, pos, list_nodes, node_size = 200,\n",
    "                                node_color = colors[com],alpha=0.8)\n",
    "\n",
    "nx.draw_networkx_edges(G,pos, alpha=0.5)\n",
    "nx.draw_networkx_labels(G, pos)\n",
    "plt.axis('off')\n",
    "# q=community.modularity(partition,G)\n",
    "# plt.text(0.5,1,\"modularity=%.2f\"%q,fontsize=20)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "## visulize solution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "hidden": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 1, ..., 1, 0, 1])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# with torch.no_grad():\n",
    "#     p=torch.sigmoid(x)\n",
    "\n",
    "p[p>0.5]=1\n",
    "p[p<0.5]=0\n",
    "with torch.no_grad():\n",
    "    p=p.cpu().numpy().astype(np.int)\n",
    "p.reshape(-1,)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "partition = {}\n",
    "for idx, n in enumerate(G.nodes()):\n",
    "    partition[n] = int(p[idx])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "hidden": true
   },
   "outputs": [],
   "source": [
    "subgraph_list=[]\n",
    "for sub in nx.connected_component_subgraphs(G):\n",
    "    subgraph_list.append(sub)\n",
    "\n",
    "    \n",
    "def plot_label(G, partition):\n",
    "    pos=nx.layout.spring_layout(G)\n",
    "    plt.figure(figsize=(5,5))\n",
    "    colors=[\"r\",'b']\n",
    "    \n",
    "    for com in set(partition.values()) :\n",
    "        list_nodes = [nodes for nodes in partition.keys()\n",
    "                                    if partition[nodes] == com and nodes in G.nodes()]\n",
    "        nx.draw_networkx_nodes(G, pos, list_nodes, node_size = 200,\n",
    "                                    node_color = colors[com],alpha=0.8)\n",
    "\n",
    "    nx.draw_networkx_edges(G,pos, alpha=0.5)\n",
    "    nx.draw_networkx_labels(G, pos)\n",
    "    plt.axis('off')\n",
    "#     q=community.modularity(partition,G)\n",
    "    # plt.text(0.5,1,\"modularity=%.2f\"%q,fontsize=20)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {
    "hidden": true,
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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kO25WiVmG/hA9B9hR5v+sDlNYStmIdhE/B1iWdC1Jyno6fuECs0mYvR+znwIbgTXA671mSz8PN55dJg/AcmFl2IlImTKzjxAmoD+RdC1p8AWz//BJ+JvxcMjCGT5tfb/rgNGHoLYJNgNLcF+fXKXpoJGllAUzmwaMBZ5JupakmNmdZva2mbUOM3uzGb46DGpbobcN9n8MJo+AszMwZxGMHwY7gabPwGNmdsjM2rP+mpr09ym0qqQLEMm36EHGVcDP3b076XoS9CXgDxz8BVh1JcycAxtPg+F/CGN7gXWwrg5qnobG2rDq55DB6Guh5V6YSHlNtfoNGllKOZgL7Ac2JF1Iktx9nbt3AldUQSPQuxGqt0Dncmj+Hrw5AboPQOZyOLwBcg90VUMNYRZB2VJYSkkzs3rgEsp0qtCRzOzWWrh3Npw8Bg5dDy2roHICdH8GTh4Jcy6B8f8Gw7Pf9zAMb4B7zGydmf1hUvUnSWEppe5SYH05Hax1LA6f3g9bHoIN18C+YeBboXojVNdD1XOw4yuw+WY45VcwDOB34Z2XYO1e2FoDNwH/K3pYVlYUllKyzGwsYWPfR5OuJUXqq6D3Kmh/C6q/DGOGQW8V+H+H9gx0XQf7FkDbA6FV5zw4eDIcqoLezjC16O+B30n0WyRAYSklKVr/fRXwuLt3JF1PinQQ/bnvhorXIDMtjCBtFOwZm3WvcgAV0fsdsPyXmi4KSylVpxNGRs8lXUgamNlYM7vBoL4FXv4RTLkPRi6Czt+CbROg869gZDfh/uRKaLgGWgHuhObd0NQLqy08LPsjwhrzsqJJ6VJyojXNNwM/c/eNSdeTBtHGGQ8AM6ugeipwI7z9GdgF8BwM+wScvAHqJkLXX8DWj8M+gGvhlCeguQ26emATcKu7/0Ny3yYZCkspOWa2EJji7j9IupakRRuHzCHsCH8QeOYuePV3wuYYTUB7DpfJAC3AonKeZ6lJ6VJSzCxD2NX79qRrSZKZjQDmEYLyDWApYamnRy9YAtxFCMJjBWYG6CEseSzboASNLKXEmNkHgYPu/nDStRRa9FBrCmEUOQV4AVgVbcs20BtmAHcAIzhibTjQQHiIsxetDQcUllJCzGwi8FHg6+5+MOl6CiW6R3sWsIDQLa4E1uS0C7xZ38qcmwij0F7Cg9/VwG3AsnIfUfZRWEpJiEZVSwgh8XzS9RRCdMthbvTXDsImIRsHvVIprKGvBzoosTPU46B7llIqZhLWL7+QdCH5ZmYTCK32GYSjMb7n7ruGfOEQkLk88ClLCkspemZWTTjW9m4v0RFRtHPSdEKrPQJ4Fvh7dz+QaGFlRGEppeBC4C1335R0IXEzs2GE3d3nE0Z9zwAvu3tPooWVIYWlFDUzayKMtr6ZdC1xio7AmAfMJhz38GN3fyvZqsqbHvBIUTOzDwPvuHvRb5YRPaQ6hRD+k4BfEab+tCZamAAaWUoRM7PJhPmE9yVdy1BE91xnEUISQqt9l7sfSq4qOZLCUopSNAq7GvhFTvMJU8jMGoHzgXOBrcBDwBvapDidFJZSrOYQluG9lHQhJ8rMJhFGkacS6v+Oux9razRJAYWlFJ1oc4jFwA+LZRQWTf05kxCSDYRVNg+U00qjYqewlGK0CHjd3bcmXcjxmFkdcB6h3d4HPAVsKNX5oKVMYSlFxcxGEsLn1qRrOZZo/8j5hDXbGwij4LeTrUqGQlOHpKiY2Q3AVndfkXQtR4oeOk0jtNrjCbu0P+fuWkJYAjSylKJhZlOBccCPk64lm4Wde84mjCS7CVN/fuju3YkWJrFSWEpRiB6QXA08nJYQilYPzSMsR9wM3A9sKpaHTnJiFJZSLM4D9gOvJFlE1Gq/h9BqTyXs+/gtd9+bZF2SfwpLSb3oifKlwPeTGrWZWSVhG7gFhKNjVwL3untnEvVI4SkspRhcSthpZ0ehP9jMhtM/9Wc34aCv1zT1p/woLCXVoik4s4B/KvDnjiM8sJkBrAfuTCKsJT00dUhSK7o/+DHCSO6ZAn3e6YRWezSwCnje3ffn+7Ml/TSylDQ7jXC29ap8fshAZ2sD67TBrmRTWEoqRQ9UrgZ+lq/QOuJs7V9z5NnaIlkUlpJW84Hd7r4xzotmna29AJhMOODsm0c9W1skorCU1ImOeL0I+E6M1xzobO27i3UvTCk8haWk0WLC+d+7h3qhI87W3g4sYyhna0vZUlhKqkRnYp8OfD2G6ywgHB8b39naUrYUlpIaWUdFPDqYTXGPcrb2QzpbW+KgsJQ0mQHUEh665OyIs7XbCFN/XtHUH4mTwlJSITrh8Ergp7kuJYzO1p5PWOGjs7UlrxSWkowwj7IO6CCE44WETX3fPPbbBjxb+xs6W1vyTWEphRM2yb0CuJEwEbwXqOg0W/s/YNdq+NOjv1Vna0uytDZcYmdmdwKXA8MJ03X+1uFp4DvtMPLTMPoeyHSDTYcDy6C1EnozsO2T8Le3wS2Es7T3A38HPE//2drPoLO1JQEKS4mdmc0kzGXsNLMzqmDFY9C6EA5dB2N6wG6DzWOh+3FoPAPqxsPOndA4E045Az7/FNxFaM3PAZYDK3W2tiRJbbjEzt3X9f3nk6CqA5peg64MdCyD5s2wZiT0OjADajLQWgH+l5C5BA78E3xqOvS0hWNjf6KztSUNKpIuQEqTmd1qZh1b4KXx0PtbsGMFZCZC52dh0gg4+3Q4626or4ODLZBZBSOGQ+81MLET/hz4PDA26e8iAgpLyRN3vxloWAqPXwttw8DfgurXoK4JerbCS1+Ets/A6OUw6RBU7QBbCsO/Bjv2hB3J3wD+LeGvIgIoLCWPHPw6mLwJ/Mswpg56q8D/HPbuhvHzgXnQ8RQcGg37hkHPVbBvEezKwOyx8L+BC6NTFEUSpbCUfKoHervBNkL96eF/b7Yf6nuhYjK8VQHdFeAAZ8IB639v7wfCPEwAe9eVRQpMYSmxMrOxZnaDmWUmQs1PoPk+GHUB9F4BbROg8yvQUAetj8KwldBwDbQC/D7s/jk0PwV1XVDxXfhvwBPaa1LSQFOHJFbRbj/3AWcClVOg5xbY/8ew2YCVMPwmmPoqVE2Err+ArR+Hw2H4NzDmqzCxHXw//By42d23JPR1RA5TWMqQRUsQ30NYlTODMHl8NfCKh/XeXyMaPe6B5kroaQ4bXhxNI3AL7g/mt3KR3CksZdDMrBE4mxCSTgjIF39jnXZY4rgCaDoEB3fCqPGwszK6TzmADNACLEK7mEuKKCzlhERrtKcTAnISsI4QkluPugTRbAZwVws0A21N0H6Uy2eAHuB63NfHXbvIUCgs5biiNnsSISBnAtvoa7Nz3MjiLrOLF8C/TIKuirCBRnYb3kB44r0XWKKglDRSWMpRmVkD/W22EQJyzWC2QzOzj06ATdvC/cibyNp1KLrubcAytd6SVgpL+Q3RKYjTCRtYTALWE8LsrcHu9GNmk4EPA//o7t3RDysI8zD79rMUSTWFpfS12RMJo72zgLcJAfnyUPeLjK79e8Bqdz+h4yJE0kS7DpWxqM2eTQjJSkJA/rO7t8T4MVMJ+1quifGaIgWnsCwzUZt9OqHNPonQZt8HbIl7Q91oVHk54bRGtdpS1BSWZSAKrQn0t9k7CCco3uX5faByBuEBjp5uS9FTWJYwM8vQ32ZXEz11LsRa6+gM78XAwzoCQkqBwrLEWDg1sW/S+GTgZeABYHOBQ2sWcIBwRK1I0VNYloCozR5PCMhZwE5Cm/3jPLfZR6unErgUWKpRpZQKhWURM7Ph9LfZtYQ2+1vuvjfRwsJJjO+4+6aE6xCJjcKyyESjttMJATkFeAV4ENiUhlFctHb8YnQchJQYhWWRMLPxhOk+ZwG7CaPIu929M9HC3u18wmqfbUkXIhInhWWKRW32LMIochhhYvft7v5OooUdhZnVAguB7yZcikjsFJYpE7XZpxEC8mRgA2HH8DfT0GYfxwXARnfflXQhInFTWKaEmY0jtNmzgD2Ep9k/TWGbPSAzqwfmE3YPEik52kgjQVHA9LXZ9YQ2e3Va2+xjMbMrgWp3fyDpWkTyQSPLAova7FMJAXkK8CrwCPBGEbTZA4qOlzgHuDXpWkTyRSPLAona7L5J43sJbfZ6dz+YaGExMLNrgE53fyTpWkTyRSPLPIra7LMIIZkhtNl3uPueRAuLkZmNJJzo+PWkaxHJJ4VlzKINJPra7GmENnsZoc0uxW3KLgVWuntH0oWI5JPCMiZmNpYQkLMJbfZq4N5SaLOPJvrO0wgbdYiUNIXlEJhZHf1tdiOhzf6uu+9OtLDCWQw8WSzTm0SGovzCMjyNrmOQB2VFbfY0QkCeCrwGPAr8ukTb7AGZ2STCuT0/SboWkUIoj7A0qwGuAG4k+whWs9XAt4BfHO8IVjMbQ3+b3UJos+939wP5LD3FFgOPD/VAM5FiUZF0AYNlZrVmdruZbTKzNjN7wczeF/2uxsx+bGZvmpnfH4Lta4Sntnvug+75MKoBPvgeuAdYgdmMrGs/ama7zKzVzF41s68DH49+/X13/7a7P1euQWlmpwAjCNOfRMpCMY8sq4AtwCXAZuD9wL+b2SxgG/DEDbB0GdxRGabt7Ox7YwZ6Pg67D8A7Xw1n0zQBd2F2vYUtz75COJFwWvSWPwNO1046hzcaXgw85u49SdcjUihFG5buvh/4QtaP7jezN4Dz3P1NzG4FVowHesLxBoddBh2XQcdSaIh+1N4NTa3wkwzc0d7/NPs+wiTyvwDeQwjhcncaYaPhtUkXIlJIRRuWR4pWyJwOrIt+dAUwwuGoS5R6wRxsO4zugcomsCdh82z3H5rZ/dE1agm7/jyX7++QdllH2y4vp4dZIlAiYRntzv2vwPfc/ZXoxzcyQFA6cBBq90Nde2i/rRHa6qDToGE2/Efgh+5+TXTdK4AzFA4AzAS6CdvGiZSVon3A0yeayvMvQBfw6eiHFYQn121Hvv4daHoHmmugKwP7DHrrQ1ASvX5O9H7c/ZC7PwhcZWYfLMT3Savon/NlwLJi3fBDZCiKOiyjtvB2YBzw4axpLPWE6UHvMgw6K6A3Ax0VA7+mN3p/tir6H/aUqzlAK/BG0oWIJKGowxL4BnAmcO0R03g6DkJFBxhAF1gHWJSCBw26t0NjV7hnSQfYwei1L0FtNVxsZnVmVm1mHyMcwPXLAn+31DCzKsKsg+UaVUq5Ktot2sxsCvAm0Em4j9bnk+7+r+PM9u88YoT4Crw0HbruhcbrwlPdw86H9mdh2zOw+YKwdHEG0ENYofPX7v7TvH6hFDOzBcBUd/9B0rWIJKVow/K4zN5PmIjeOtCv90NdK2TGwa6s4XUjcAvhPqUQJvgDfwTc6e7bk65HJCnF3oYfyy8I8yUzA/2yHg5UQXdr/1zLTPT6ZQWqr1jMJxyWpqCUsla6YRnWei8htNLvCkwDRkDLfqjvgubodUuOt0a8nES7Kl1A2ChEpKyVblgCuK8HridsfNFI/ygSgCoYPgp6d0PlHrgher30uxB4pZR2dhcZrJKYlH5M7usxW0RYeXIT2bsOwepquG0mjNoHY0r07u2gmFkGmAv8c9K1iKRB6T7gOZowubqerP0szawB+BThIcbbSZaXFtEOTu7uDyVdi0galHYbPhD3Xtzbszf+dfc24GHgQ9FRtWXNzJoJ+3Y+kXQtImlRfmF5dC8S7m1enHQhKXAJsMrd25MuRCQtFJaRaGXKfcBcM5uQdD1JMbPRwHTgqaRrEUkThWWWqB1/BLiujNvxy4CnSvlUSpHBUFi+2xrC7kOLki6k0KIR9RTg2aRrEUkbheURstrxeWY2Pul6CmwxsMI1MV/kXRSWA3D3VkI7XjZPx81sMjAWeD7pWkTSSGF5dKuBduCipAvJt6zjIh5z9+7jvV6kHCksjyKrHZ8fne9TyqYSTrNck3QhImmlsDwGd28h7F5Usu141qjyUZ0zJHJ0CsvjewHoABYmXUienEH434E2ERE5BoXlcUTt+L3AAjMbm3Q9cYoOIVuMDiETOS6FZQ6idnwZoR0vpX9ms4ADwMakCxFJu1L6g59vvwIOEvZ4LHrRPdhL0ahSJCcKyxxlteMXmtmYpOuJwbnAHnfflHQhIsVAYXkC3H0fsJy/SJ6wAAAG8ElEQVQib8fNrJqwu9LypGsRKRZF+wc+Qc8DXYSzaYrVPOAtd9+WdCEixUJheYKy2vGFxdiOm1kt4b6rRpUiJ0BhOQjuvpdw4uF1RdiOXwBsdPddSRciUkyK7Q96mjwHdAMLki4kV2ZWTzgH/LGESxEpOgrLQYra8XuAi6LdxYvBRcDaaGQsIidAYTkEUeg8RhG042bWCJwDPJ50LSLFKNV/wIvEKsI55POTLuQ4LgZ+FR2dISInSGE5RFnt+CIzG5V0PQMxs5HADODJpGsRKVYKyxi4+zuE9jat7filwEp370i6EJFilcY/2MVqZfT3eYlWcYRop6RpwDNJ1yJSzBSWMclqxy9OWTu+GHjS3TuTLkSkmCksY+Tue4AVwAejHcgTZWaTgImEh1AiMgQKy/itJPxzTUM7fjnwuLsfSroQkWKnsIxZdI7NPcAl0VPoRJjZKUAz4VgMERkihWUeuPtu4AkSasejz1xMONq2p9CfL1KKFJb58wxQBZyfwGefBtQCaxP4bJGSpLDMk6gdXwpcamYjCvW5WUfbLtfRtiLxUVjmUdSOP0mYrF6odnwmYTekDQX6PJGyoLDMv6cJ7fjcfH9QtHroMnQImUjsFJZ5lvV0/DIza87zx80BWoE38vw5ImVHYVkA0a7kT5HHdtzMqoBLCPcqNaoUiZnCsnCeAmqA8/J0/bnAdnffkqfri5Q1hWWBZLXji+Nux82shrAL+qNxXldE+iksC8jddxIe+MQ9WX0B8Ka7b4/xmiKSRWFZeE8Cw4Bz47iYmdURwlKjSpE8UlgWWFY7frmZNcVwyQuBV6Idj0QkTxSWCXD3HYTlkENqx80sQ3iw88u4ahORgSksk/MkUE84cXGwFgFr3L0lnpJE5GgUlgmJdgNaClwRHVN7QqIn6rMJuxuJSJ4pLBMUteMrgWsH0Y5fAqxy9/b4KxORIyksk/cE0ACcnesbzGw0MJ0w0V1ECkBhmbCsdvzKE2jHLwOecveD+atMRLIpLFMgmkz+LHDN8dpxM5sATI5eLyIForBMjxVAE+GhzWFmVJqRMTv872ox8IS7dxW6QJFyVpV0ARK4e4+ZLQU+ZvbbW+DuBcCNhG3XeoEKs7YN8PnNcPLdiRYrUoZMu3mli9mfLIHP/RmM7QVzoC38xoF9k2BYF9RtB5a4sz7BUkXKitrwAjKzWjO73cw2mVmbmb1gZu+LfneymTl889swdSoMnwafzfS/+7SzYNI4GPUeGH4+VK0zG/Fo9N7RZvakme0xs31m9rSZLUzmW4qUJrXhhVUFbCHMkdwMvB/4dzObBdOq4XWg5TXo7YTdI2HcrvA2B57YDg3tMPxg6MpPng2fnWxGDdAO/D7wWvTi64D7zGysu3cX+kuKlCKNLAvI3fe7+xfc/U1373X3+wlHQJwHX+obCbZD7SEY3gF7m0P2dQwLv6qPpgo9mIHdlfB7vcDl7n7Q3TdEm3QY0AOMAEYW9AuKlDCFZYLMbBxwOrAOzvhI+Omk2TBuNvzBKHi7GvbXQWsDNLaFHAT47mh4315o6AVuyrrei8BB4F7g29H+mSISA4VlQsysGvhX4Hvgr8KU6fDLl2Hri/DcethfATc3we5RISTrOsM72yrgwRGwZA/h4c+cvmlF7j4baAQ+itaMi8RKT8MTEB1Z+wNCsF0HXgusAfb2v2pzFUw5G7augzGHoLon/PzWkfB/JsGWl6L/rxsBnO1O+xGf8TJwg7uvKcBXEil5GlkWWLRC53ZgHPBhdz8EdPCufxd9LXdtVlAC3DkKrt+T9fKK6P1Hqgamxli6SFlTWBbeN4AzgWvd/QCAO73w4CZ4aWR4NrO9Ej41Gea1waisoHy9Gp5thBv7dkVvAFaDzTOzi8ysxszqzOxPCWG8sqDfTKSEaepQAZnZFOCTQCewPWsZ+CfhIythxULYPQUyPXBRK9z169+8wrdHwdntMLOz75LAbUAt8A+EkeQh4CXgA+6+Le9fSqRM6J5lSkTzJfvWh+eyR2UGaAEWuaN14iJ5pjY8JaLAW0LowzPHeXkmet0SBaVIYSgsUyRa6309YcTYSLgnma0h+nkLcL3WhosUjtrwFIpa8ssJE84P7zoErCbco1ymEaVIYSksUy6acF4PdISn5iKSBIWliEgOdM9SRCQHCksRkRwoLEVEcqCwFBHJgcJSRCQHCksRkRwoLEVEcqCwFBHJgcJSRCQHCksRkRwoLEVEcqCwFBHJgcJSRCQHCksRkRwoLEVEcqCwFBHJgcJSRCQHCksRkRwoLEVEcqCwFBHJgcJSRCQHCksRkRwoLEVEcqCwFBHJgcJSRCQHCksRkRwoLEVEcqCwFBHJgcJSRCQHCksRkRwoLEVEcvD/ASqYuv7Yz1dhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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TtD2ReEFMARE5AEsbeUBVU3XbkiVdCxHgPWCom/CXMqq6AhtLMFZEjosnLK7F2FjgxXTuG0aqKTcAOGu+FcsV9Xh24gUxSURkP6zC4sEkG5mmS9qCGJSV6K7VhFW17AN8w6UFdcVJJDZBL1HScZdDeLfZswteEJPAzTg+AxPDFVm+fRAWIthe4l4i0pjuhVR1MzbVrx7bVyyJPEZEhmINFRKZoJco6QRUQnhB9OyCF8QEcR/sc7ByvFQ6s6RLIILoEsbfIY2Ic5TrPQi0YRHoitBzYRP0Xkpwgl6ieAvRkxG8ICaAa556HjBRVRfnaBlBWYhge4mBWImwcyzBE8AK4AoRqXVPHYoFPhKdoJcoqVaphLMCqA+6LNFT2HhBjIOb9XE+8KSqLsrhUgITRGfVvUsAe4lh11TgBeAjrKplD5KfoJcoabvMTsSX4/sjesLwghgDV5VxEfC0qn6R4+UEaSGCCeLeItIQ1AVdVctUbFDUfwJLgg48OZe8hNRTbsLxDWM9nfCC2AUuNeVirLX9vFyvh4AFMRNWYhirgJVYueDeAV+7gTRSbiLw+4ieTnhBjIKzmi7BggEf53o9jqAtRDBB3CdIKzGs8evD2FiCc1wSe1AEEVAJsRjrF+kTtD2AF8RdEJHewKVYJ+fZuV5PGIELouvK8y7WjisoxgDtwGxV/QpLyzlBRMYGdP0gAirAzrShFiCtRHVP98ELYhgiUgdchnVj+SDX64kgExYimCDu69pypYWIVALHEzZBT1VXYVUtB4nISQFYY0HkIIbj3WbPTrwgOkSkBhPD91X1vVyvJwoZEURnJb5HMFbiscCnqro84h7rsbEEewJnpTmWIEiXGbwgesLwggiISBXmJs9W1bdzvZ5InFVVRvLdshPlXWB4Olai68g9EpgS7XnXJ/J+oBq4wI0RSIWgLUQfafbspMcLonPzLgXmAW/keDldUQK0BTi9rxOqugUr6UvJSnSCfRpxJui5WupHgM3Ape6LKJn7VGLv2c2prLMLVgG1ya7F0z3p0YLoqhQuBhYCUzKQQBwUmdo/DOcdzEpMpQNMwhP0nKj/E/gS68DdK4n7pNXlpov1tANL8Vaihx4siM5l+zawDEuvyVcxhCwIorMSp5Oklej+jidjgZSEJui5BO6XMQG9MommtUG7yyH8PqIH6KGC6AYMXYhtzj+f52II2bEQwVqD7e9SjxJlPLDIpdgkhapOA17FpvolIkhBB1RCeEH0AN1YEEUoFqFGpPNrdC2qvoWVfj1TAGIIJoiZCqjsJNm9RJfQfTDwchr3nA1MwgItw+McHlgOYgRLgYFxejp6egDd6g0gQpkIp4swCZgPfAh8IcIke/zxCqxrTSvwVBpD0rNNtixEsL3EEQlaiYFM0HNjBR4CzhCRMTEObSADFqL7IlgPJDW72tP96DaCKMIBwJvAH4AR2Aenyf0eAfoHOOYjuGgw8HimIrYZImuC6KLE04GjYh3nJujVE8wEPVR1KZareIyIjO8igTtTFiJ4t9lDgQiiiNwsItNFZJuI/C3s8RH2ePF66DUbjhoJM7YDzmJpB24YBL2HQf0w+MkAuP8y0OHu/DNEZI6IbBKRt5OdJJdFsmkhgu0lHtBVBNhtO5xGcBP0AFDVtdhYgpHAqeGi6NJiirBSu0zgBdFTGIKIRYJ/iZWARTw+7ELY8Sms/RxOXQsX7tXx9H83wuR6eG0xvLoUXi6GPzQA94kMGYF1er4e6A08AzwdrQ1+HpBVQXRW4gy63ks8EliZiZZozv2+D+gPnBtW1dIHWJvBPV8viJ7CEERVfVJVnyJi/8jGf87fB4rqQTdBscLisA7IDzXCteuhv8CY1XDzSri/BqiH/W4G3lTVqaraCtwKDCKg1voBk20LEeBtoliJ7v+PILgJervgygkfAIqBb7t80Uy6y2DvrfKwbt+eHkhBCGIcroG6YVB5MPxoMHzHDX9S4PNKGNEGfddCkcLBLTC/0p48eBwQvk8l7mdktl9AAmRdEJ2V+AG77iWeDLwX4AS9ru7fCkzE9oEvw76sMpFyE7qf4sv4ejwFLYgupWY0bJgJ62bCr76Cg9we07pesKUI9mgyyxGgvg1aiqB9I1zQgG3gH+uSi/8DqxfOxxKuXFiIYFbiSNcFKDRoaxDwVjZu7rIAngU+x7IDghxUFQ3vNvdwCloQMfFyqTN17fDvq+H6obC0BJp7QyWwsD+sbICmOlhZBVXtZgiO2gb9rgP+jM3WaATmYlZCvpETQXT9Aj8AjnJ7eacBLwY8QS/eGlRV/4UNhTrZjXXIFF4QeziFLogtdHoN7cDWIlhUCnsshWE74FNgawVsK4MZdTCsFZb2hw110NyEdcYeCfwca0/1fvZfRlxyZSGCWYmjsL3VjdgfNKu4aPNG4Cls1OmQDN1qKdA/TwNrnixQEIIoIiVuuFAxUCwiFfamlRNgykJorYV1RXDNHlDXCmO2QlkrnL8G7q2DLU1mBN7dG85fBwPc/tj2vsAwXIdsbFzmviJymIjskUaLqqDJmSA6K/ETrO47ExP0EqHS/Z4JPA5MyESKlOvGswYYEPS1PYVBoXwT/hj4adj/X4xZdB/DWftA+yAoa4OvbYZnPocq96G9ZRksqITDhwMKF6yFa1qguR6euRu4Bvgatjf1BPBfWArOAKwVfqOINGNquiL021U2ZJNcWohggqQ5XEMDHSk3C0XkASz6XK2qQVv0SzC3OVfztz05RAqjlLdrRCjDKlR6EXU0ZbvAykao2Qy1LUANbN8M/W+FpiGYi/xONJFz+2Z9MYEcgOXG9cf68YUEcjmwXFWDGIsZFRH5d+COTN4jxr13x+ZSz8N6Mk7OwRoOBPZW1SfCHqvHtjs+wvowBvJGdgOx9lPVx4K4nqewKBQLsUtU2S7CFViKRg27iGKRQmMTrGqAilIo3Q5ll6ium+s6RB8FfFdEZgDTnIvorq1tmPCtwNw1XAOAPnSI5FhggIi0EiGSwPqAPqg5sRDDJui9AnwB3CQiU9OtXU6BXdp+qWqTiNyDufI1IvJcQLXpi7HgjRRI4w9PgBS8hRhChBFYhUM95t6Ff2hrYWu5pbHtOEt1yIedz5XewDgsuPIhSTYscMLRiw4rMiSWJewqkuuS+eA6K/VHwC+y/QEVkYOwrYN7VVVF5FQAVX0hy+s4D/gs2hREl7R9PvaF8YTLX0znXgL8b+Cvlvjv6Ul0G0GEne7zCcC1wGgs7FwEzALuhoYKWFeMfXB2eeGuSmEccCAwBxPGlD8UbnBVpEhWY0PcQwK5AljVVU2wq+H9jqremuo6UsG1678JeDA0NMr9fW4Ebsum+y4i12J9K6OmRLkvjXOAWuBhV+mSzv3OB+aq6kfpXMdTeHQrQQzHJW1XAS2qlqvoGsNeBUxX1eldnyvVmCt8MBZhnaqqgZSNuWh5uEAOwAI5a+gskitVdbvbK7tMVf8QxP2TWOfpQJGqPhvx+GlAu6pmrHQv4n4C3AL8IVYwyx13KjAE+Ec6br2IHAn0VtXnU72GpzAp+D3ErnAiuKnzY7pDRCYCV4nI0shxmWHHbQZeEZG3gcOBq0VkPlb7vDq9delWYJH7AXYK9W50CORBdES4twCDXJXI8nStn0RwE/QOAG6L8vRU4EYReStLVmIVJsAxI/vOpX8Bs/CvEpEHXPecVFhCfpZwejJMt7UQYyEiI7GB6ncnIjDOqjsUa2qwCHhDVVdmeI2hCPdBwElYNDUU4Q5PAwo0wu0srcuBj7qyop2V2KaqLwV13xjrGQycoqp/SeKcMdjWycOuz2Ky9ywBfgD8xuUmenoI3dZCjIWqzhGRPYEzRWRivGCFE803ReRd4BCsWmIJJozLMrTGNmCFs0zrVfXBLEW4R2I13R/EOOYt4AZnJQY5EjQaSc9RUdWZItICXCQik1xH7mTObxWRlcBAwix5T/enR1qIsNMKuAqYqarvJXluKWa5jcPm+r6uqhlJ5BWRUcBwVX28i+cDi3C7ypybsY7iMYdGuT3GHWrT8zKGiByPucyvpXDuYCwC/WK0CHWcc08BWlT1zWTv6ylceqSFCDutgNB+4pJkLD3X3OBdl7t4INbItAkbdL8o4PSYmDmI7l7N7ueT0OMREe79sS2Camf5hIvk6rAI99HAwnhi6JiKWYlvZ9hKbCDF+mlV/UpE/k5HVcu0JE5fjGUqeHoQPVYQAVR1nYg8h9XG3pVswMLlvM0QkVlYA4RvAJtF5A3gi1wmZbt9xc/dD7BLhHso1vm6t4iswQJQhwO3i0hZvL0zVd0gInPcNTJpJabVGFZVV4nIvdg2Rw3wSoL/LouBb/gE7Z5Fj3WZw3HuXy3wWDpvfrfHdwBmaW3HLMbP0rzm8VgA4/VUrxHn+qEI9xWY8K7HWqGFarh3BnAivzDEumdfD/xJraFs0GsT4IfA7+NFmRO4VhVwEZbe9ExXeZ8R5/wv4P40otWeAqNHW4hhvARciVlIKU+Rc/tzHznLaX/gOOB4ZzHOTVEYy7Gu0RnBpSJVu3vcoaptUWq498faYu0S4QY+xqzEVzKwvGqgNV0xBOsALiL3AxOA810wLV5fx1B/RC+IPQQviHTaT7xaRBankqoRcT0F5orIJ8A+WC/BY0XkTWBOkjW3Ga1jdsGlU4FnQ1aTJlHDjb2HRjpLcxHB1nAHOkfFJbo/ApwBXCYiD8WxbEOCOCuoNXjyG+8yhyEi+wOnAHcFYZWEXVeAvTBXuhbrzjM7QbftfCwncG5Q64m4/tHAAFV9NIVzQxHuC7AE6hUEVMPtrj8GGKKqk5JdWwLrPhHYF6tqWd/FcQOBs1X19iDv78lfvIUYhqp+4vITzxKRR4PaTHfX+QL4Qqzb89HYPJe3sLSfWA0JMmYhSscEvbtTOT8U4XZW13XAU841TSXCHY2MTNpz635ZRDYBV4rIg6q6KsqhK7GgU0U2KoQ8uccL4q68jO0nHoENbA8UVV0ELBKRPbC5x0c7YZzRxZ5WGZlzmU/BJuil1dVFVZtFZC72N5uSQoQ7XCRXhv0dGghLJQoaVZ3m9kUvE5FHInNJ3X7qcmwSX1LJ3Z7CxAtiBO5DMBG4xu0nZmTolPvwPSQiAzCL8SgReQd4X1XDBTAjFqKI7IVVYgTljr4JXCci06JtN2jyNdzLseYaX2bSQlPV2a6q5QIReVpV50UcshjYHZGFWOfwFoLpu+jJQ/weYheIyH7YlLk7g9xPjHG/fpgw7gW8C7yrqltF5PtYb74NAd6rGEuXmaKqgVlgInImsElVp6S5tlCE+3vYkKtGOmq4w9OAgqzhHgRcCLyqqjPdg2UvwWVD4bp9zFoNbyf3F+AVfK1zt8ILYgxc+VYD1iQgK38oEWnEunjvC0x3/31rhNWY7j3GAntjAYXAXpdYq7JrsLzEdPMGa4HrVfU3USLcIde7lV3TgFKOcItIAzaWYMZ2WFcK97ZDn7XQuxG+lI5Da7FZtk3AFWQo4OXJPl4QY+CslSuAT1Q1K8PZw+5dj4nhd4DfAm8HYRG5gMeNWBfsNeleL8r1zwI2qM1STuc6ewInquo9XTwfq4Y7UiQ7RbhF5Gaso88o7Mvucvf4EGChwI4KKBHgRlj+fWhrgHVt0HYp7DkZ6iug/Xuw7ieW6D1BrLP4XWFLLMJc7ENUdUY6fwtP9vB7iDEI20+81u0nJlLjG9S9m0TkJay7Tgk2z2Q21sU7Hff5RGBWJsTQ8Qa2/zotzX2/mBHmNGu4W4BfYW3VKomgBWZtgd3bYEsDNK2D3tug7BaoXwDlC2H2Yig9GYaPhO3nwH0K41F9MGwdlwM/IXbXIE+e4QUxDqq6XkT+iTVwuCsTJWoxKMesreddUvdYrKHCx5gwJlXB4iLbw4A/B79Uwwn5PCzi/Foal2oghQqRBCPcle6/BwMVInIoJpQlAMXQuxcsWwv1q23uxNZtUDYRGu6ERX2hrS+0fRtW3wPV59gcnxOA8ImEl2Flf94FKyAKYlB9rlHVz7AZK+c4Vy1b7Iwwq+pGtYasf8a6aF8rIme7fa+4uH2404CXg9yP7II3gcOcEKVKYDmIqrpVVRep6jRVfVJVb8NmcM/HrMUBwNexXEp2h2ED4MDroX4N6EaoWQEVq6EMmaIqAAAgAElEQVT0UDsegNGw5TOowIaaXRt63Ln7RwP3B7F+T/bwgpg4U7A3/7gs3nOXlBtV3ayqrwJ/xNzFq0TkXBeljsUYLAiR8cFJavNnPsNqw1MlJQsxUVyu40Zgrao+rap39YdfvgErP4VPp8DijVB+NQzcBuXLTaBpgJ2J5L2hbTMUu+uMxr50AC7Fxk0szNT6PZnBC2KCuIqKx4EjnAWQDbrMQVTVLWpNU/8Hq6i4TES+5fIaOyE2Qe94bHJdtly4N4HDU7ESnRWekSqVWCyHtvGwuR62HADr/gKfT4PyTaBVZgWyEOrb3OdmPRRVdwhkO1a+CCaIf8/m2j3B4AUxCVzNa2g/sToLt4yblK2q21R1KiaMi7G2+Re5vLoQx2HddlZkbqm7rGstto+XipVYA2zPgmsfSQvuM7ENSpucVVgOW/eEpkZo/RDKVkDfjVA1E6r2hVDgqAhoEZFxWMJ71A7nnvzGC2KSqOrnwGzgm1nYT0y4SkVVt6t1hP4fbG/sWyJyiYgcgvVoTCsNJkXewKzE8iTPy6i7LCIlznItBopFpEJESgQOfQcWNMNu86Dxh9DrMNhUA0VV0HIObPi9pfo0z4C6B6Hft23bohaY5SpYLsPmfqc8BtWTO7wgpsYULCI5PsP3SbpsT1Vb1WbE/BHrVfi/sL6C/bMcEApZifNJ3krMtLv8YywwdQtwsfvvHwNHHw+HDoRBJ0C/CthxD6yqgpZSaP0pNA2BbcNhxLmw2w2w5mgo3Qg1y+HvTmS/hXeXCxafdpMCqtouIk9gkd6vXMOGTJByHbPLodyB7eW9A5wObBWR14H5WdxLfAO4QkTeTcIFznRA5WfAz0L/7yL1pwO1e8GYOfAQ0KsNWpZDv1pYvwNKSqByYkQ9djvUNoPuazmPy4E+ybY58+QP3kJMEZccPQnbT6zJ0G1SFkTnpp4EPKeqs4DbMWE8CRPy/bNhMboE8C+Aw5I4LSsBFec6H4tNX/wCuGuO6hdYdVLbVmiohK0l0F4CbW3mYodTUwStfeCbm+AeYD/sbzs402v3ZAYviGmg9uGZie0nZuJvmU6nm9AEvcVgVq2qzgHuAF53z98gIiMztPZw3sCi84nuJWZcEEVkGFbCuBvWEPjtnb0ZVeeugAvXAb2sZrk2JIjOrK4F6rD5MxNQnev6Kd6PTSM8T0TOyeAXpSdDeEFMn9ewv2Mm9hNTEkTXIGIMUabhqfEp1hT2Zayi5EYROTBTwuisxAXAofGOzXTKjYjUisgEbIzAC6r6qEbpmD0Ayr4GPy6xOdVzBRpqoLzdOvHMxTrxjA9v7OD+tnOA27AphjeKyBFZ+MLxBITfQ0yTKPuJQSbjJi2ITlBOBabGagbh9hA/F5H5WDnb0djcl6lYrXPc8QZJ8gZwuYi8p7FbZtUC24JOuXGidBj2Omdg3b2jDplyx45thqdR/RKYjEjRgXB1M0zZoBqzWaxb+8ti42lPA8aIyPNq1/LkMV4QA0BVN4rIJMx1vivAPn2pWIj7Ar2xnopxccK4AFgQVnIW6uI9syvRSBZVXS3WZPVQIFbnoMADKiKyO1aatw24T1VXxzllOBZ57mjmodq+2BpE9Er0vu41PwCMwN4bX2Klkz4lJ0/xpnxAqOoCzPI4N0AXKSlBFOtAfSowORULT1W/VNUHgMewJhDfFZEjRaQs2Wt1wRtAvOsF5i6LSKWIfAMbgjUN+Hs8MXQW9jis3VpkJL4Ja+SQMM6N/hhzozdg+7ZjXWs5T57hBTFY3nC/jwnoeslaiEcCK1ywJ2VUdamqPgw8iM0T+Z6IjE8hwTryuquwlJVYe4lpC6IYBwI3YSV3t6nq7ARTjfbASvA+jfJc0oIYwiXOvwLcizXnvc71X/TkEV4QA8Tlnz0BHOSimOmSsCCKSG8sQPJiAPcFQFVXqOpjWKJxP0wYj3W10anyOjA2hpWYlsssIn2xapEjsOavz2ly3btD1mG0XMJmbDsiZVyA6R9Y5dA5InKeiNSlc01PcHhBDBi3f/gk9mavTfU6znUrBxKd2XEy8I6mOUEvGqq6SlWfwHLtemGu9Imp1HM7K/ErrPFtNFKyEEWkVEROxHU4B/6iqkuTvEZfzCL+sItDUrYQw3Fu9CdYK7d1wPUiMs670bnHC2IGcJHm97F8tFT/xiVAu8ae2QzsnKA3ABvIlDFUda2q/hNrlV8B3Cwip6Qg/K9je4ml4Q+mmnIjIvti7nFv4A5VfTfFapEjsbGsXQWSNgOlQe2pquoOtYFc9wBDsP3FvYK4tic1vCBmjjex1lDHpXh+Qu6ysypOA14MKiIcD1VtVtVnsSTvIizf7nSxwfeJnL+S6FZiHbAlTlrOTkSkl4hcgM2XfkZVH081gutEfT/si6yrdYfGFqRtJUZcdy1WLvgKcKaITPBudG7wgpghwvYTDxSRvVO4RKL7h4dhFROR84QzjqpuUNXJWAR1B+b6nSk2ICserwPjdlqJIsUnw+6l5pbGRESKXZut67H64TvSDSRhDShma/wREYELInRKmL8NG1x1vYgc5d3o7OIFMYOo6mZsP/HsFL7x4wqiKw0bj1Vc5Gx2h6puUtWXgT9hFRrXuNK1xhjnrOwNyx6Em7Eczvn/hBeb4NeITELkdKK4pq5O+DpsfvVfVPX1RLYVYuGi5wdhtd7xaCLNwEosnBv9L+Cv2MyXGwMK0HkSwI8hzQIiMh7YB/hbontbIjIUOEZV/xbjmLOBzU6M8gbXButw97MAa6e/MuKgA7bBA5tg93poKoKNTVBXBO2ufrjT3GMXwDkRy498EWt4G8ibV2xO9SBVjdvU1R3b21nGGUdEhmO5pSuwL75dygw9weEtxOwwFYsWH5/EOTEtRLEJenvRkfuYT1wN/DfwC+BK4BIRuUBEDhMRLRbZXA2z+8DoX0DJJmu/zyYouRJ2q4G9G2HoL2CIwsSfiZwL/Ah4CvhPrApno4j8JN2FOpf0CBIPSKWdepMMqjoP61S0AstdHC8ivsIsQ/g/bBZQVXWlfde5eufPEjitS0F0kevTgVeCrvkNiGXAL7FgRyXWxftgrKECzfBZrT2+aRuUroE+NbD5F9CwCIrD5x7vDaXXwW/ugItXwQ8x6ywtFzmCkdgg+2UJHh9I6k0yuGDZ62JzuU/BotGTNU5NtSd5vIWYJdx+4uPAWQlGY2NZiGOwIEbGJ+ilgtqoz6dwCdZuX+wd4G8ALTBoFZRvhbIy2FEGOzZB9VNQ8x+wrAHah0LZBGh5AIr7Q+ufbMshUFyaz5HErq2OpBno7c7NKqrapKqPAC8ApzurO2vWak/AC2IWUdWvsJra8xKIHkYVRMnNBL2gaAM4EOpHwe4Xwl4fQ99y2PYl1K2Goq9B2wro1wZFh8Da+VAqoPvDRe4aX4rIEhG5L1bQJkFCwYqEI9SqutW9jqp4x2YKtbk+t2OW+LUicox3o4PBC2L2eQub1HZCnOPKiG4hHk+WJ+gFxV6w9i1Ythg+nA4fb4Ht10HDRqhZY5P2KILqPjbhrrkPtIbmHu8Jw8stxWhPzP2uxWqt06GrJg7xyLrbHIna7Jw3sL6W/bFo9L65XFN3wAtilnEfvknAAS6C2BW7WIgi0h9rJTUlcyvMHNdC5SHQugWqq6D617D5bajeAFJnWwA02/jPXuug1xqoqHIBlzpr6f+JE4KVWOPWk1NNYBaRgVjd9JwUTs9qYCUWLkn+UeB54BQRuTDBPFBPFLwg5gCX/Ps4VpXQ1QerkyC6PavTgSlJNivIOiJSJjYXejdgkIhcKiL/58dw1VaoaoWSMthRBxsB+sHqPaG5Edo+hbY+0FwCrbOgdm/Q5dB3M1TXwJ5h9dMhqy7VvbwjgWmptEkjDyzESFyA5Q5gCZYHemxkaaQnPn7fIUeo6mKxJqwTROTeKB/MyMYOo4BSbIZLXuCi3X0w4esX9rs3Vo/cB9tvmwEsb4V9PoXjD4bBq2Hbd2HPw2BjA7Qtg7JzYe3vofFYaF4FbY9B9e2wqBGKnoS1m61EsUxsmuA3gPdwlmWS667HUpaeSfGlN2Nual7hou9vhkWjbxSRF4DPCnC/OSd4Qcwt07A9sRMJb9slUrwH1K13gigdE/QeS7FpQVo467SWDsELiV8DVpmyEliFuZ8hd/ZPYZc4Bfg5MO84GKXQrxpaj4INE2FBG0g7FP0OllwCZcNhRDm0fQdWTLCmqnVPwUtYA4d+7p4zsUa23xORZqzP4kLgywQs6COAD9JIWWrCxo7mJS55+zFX4XIacIhL08n4JMNCx1eq5BgXNb5uKLy6wJqTXgOMXg811bClBGbcDdN/CPPWJlBJEcB6Kuhs7YX+uw0TvZD4rQJWJdqIIewGZVjji16YsLEFyjdAzW6wVu3CDZWwpQ5asGDLemyg0y73ctH6AdhcmCHY33AdHfOTOwmkiFQB3wFuT6MRRCNwkar+MZXzs0lY4vk4YDpWNZSVJiCFiBfELCAiNwOXY27vw6p6uXt8CLCwCLaWQ7kA34F1/xcWLTcrqulaGPos1FRAW3/43RzVH0S5/k+xwesnua7MiaypBGhkV/GrBFbTWfxWujzKYBAZAUzEIsib1kNNOxTVmzXIdihZDQ39YUuxucQTwqfbxXldxcBATByHYv0N19IhkIOBKtfGLMXlSwmWJP7/5cJiTwUXfDoZ+3u8AMzzbvSueJc5O0RWbnRiKyzYDtUbgX7W6YR2kFtgt8+g9CP4fD2UngTf/4bIF8+q3h0617lF52FdX3bBubu92XWfrx5z/ULW3gz3uynjHxTVudgo0PuAeoWasrAeiGVQ2QtkHdA3CTG0S2sbsNj9vOkEchAmkOOwv9UrInIyHRZkUq6zqraKyGasXVngDXkzgapuAB53NfKn0+FGBzrQq9DxgpgFVPVJABE5BPuGBmAYlLqM4OIqWNMC9c1Q1wc2KMjj0PBbWDcENgpwCdTNs24wfwtzH/8M/ABL1K1wDUbDXd2+WN5jyNr7DHNZ1wRcApccJorj2+CEJfBf+5u4VGKZD7Pa4N5hMHwjtKSjzk4gvwK+EpEWLHI/FRPIsViS/Go6LMivEhTIUOpNQQhiCFVdKCJ3Yo03rhKRGZgbndzWRzfFC2IO+TWM+xYwCPYS4CjY8P+a+7x9LRSvhpIjYW0or2QUrH8edl8Pp/QW+QD4NvahbMQE5WxMCFdiFuMsYHXepumobi+xSPsDj8FvJ1j1Rwuq7b2AjTYz+usicmeK6TE7cRHxI4F/qs1H/hKrDy7BvqSGYBbkBBEJDcNahAlkNLEIpd4sSmdducD9Ld8WkY8wN/omEXkRy/Ps0W60F8QccgJ8cyp8eRisWQEl18Dgm6DuEaDZ0m5ohB2boWIHlJZC5SYoWQS3Ym38/w34LjYDZCPwSKJ7iHnEIGDpBNuLi5xn/SlWlXIEydUbR2M4FqT5KvxBZyUvcj+hUa4hgRwPDBCbxxw6ZrETyLxJzk4VF1R6wu1lnw4c7NzoNTldWA7xgpgrRIr6wKhxbs9wD2i9G77aEw5shZXFltLCQmjYHbaVWoVHayVs/xpUCgxWuDPUw09ECvWbfSAQdRiU6xL0PHC1iMxJtReg20cdB7wVzwJyEdiF7ickkHtgAnkMJpArMNe+RESmFnrUVlUXichd2HjYK8W8jzd6ohvtBTF3VOHK0kKEXOMa2DQINjRC2TxoHw1NAnwMtcNhi0C7wEkKA0XkRndaXyz37FZVvTWLryNdBhGjU7WqrhOR97AmqY+meI/B2P5k0mMWnNgtcD+IpQ3tjlmtJwH1TiAXYhbkkkIUSOdGvyMiH2Ov62bnRgfWiLcQ8IKYBdw+VQmWZlIsIhXnWaVGZR20jIRtq6H4ehh8GGxshLYSaD4Hyn4L/Q4EbYHND0LjHfahK22E41d1/vd7H/g+kJVOzkHgLLcuLcQw3sJ6AO7jOr0kyzisTC/tFBlnNS0QkbVY/uOfMAtyKNawo5+ILKezQOYueJUkzo1+UkT2pCMa/byqrs7x0rKCF8Ts8GPgp2H/f/Hj8PNxsPS/4cA1UFwDbaHKDYAq2PID2HQLtB0Ku5cDN8Dqc62Gd9bKiH0eEWnDUmYi9+HymT7A1ng5jqq6Q0QmA6eJyMJkBEZs1vJALO8xSDZiVqeqDbj6wt2vnA4X+ySgr4gso6OSZmkhCKSqfhnmRl8hIrOA1/O0IXFg+MTsXCJyOvAHXEJyJCugsRdsqITt26FkLdRXQdkmuHGQ6qTsLjZ4RORrwH6q+liCx5+PJYm/lsQ9zsK+KAIftSAi3wUeihWEcAI5mI5E8UbMIl5Eh0CmFUHPNGLDzE7E6r9fBuZ0VzfaW4i55RUsfWNnGVs4VbClBaoqYXsZtPaHLc3Qsh/su0lkhCaRsJynDCK+uxzOC9gYhtmJ1OVKx6zlP8U7NkVCqTddCqKzqD53P6HSyJBAngY0iMgSOgRyWb4JpPM6nhKb4/N1LBr9vKquyvHSAsdbiLkmoowt/KlWKFoB/QbCyiKoxuqJJ4hZlOdgFTDP522eYRxE5CrgVVVdlMQ54zBL68F4VoqInAiUaoYm5InIGcAKVe1yuH0C16jAGnwMcT99sBZei9xPXgmky+c8BIu4zwZe605utBfEfMBE8T7M2lBcn0CAZhhYAdsrLNn6ilAZm0sHORHruvK0FtjAIVdSdwvw22Q+UO6867G+kJ/EOK4c+B5wt6pmpJpERI7C6qJfCvCalXQWyHqsDHERHQKZ8/pp6RgLuzfmRn/UHdxoL4j5gqVznABcC4zGUnKK1sCCv8CMH8KPu+j2shdwFuaSvVQouWMiMgD4pqrelsK5QzAL+bauXq+IHAkM1Ax2CBKRA4CRrmN1pu5RRWeB7I0lly9yP8tzKZAisjvmRm/HvJWVcU7Ja7wg5iPmllQBLWL7vN8H/txVBNm5XadgH5inXGlaXiMiBwODNcXgkIh8E9ioqi9Hea4Ysw4fVtWoTS+CQKwr+DdU9a5M3SPKPavoEMchWMlmuECuyLZAOjf6IOA4rCfmv9SGcRUcPqiSj4SVsSlsF5F52PzgqAnM7s33T7EZLee5GtUpeZ7ekWxAJZKXsI7Qs6LkyI3EmldkTAwduZjR3ALMdT8h13WI+xkD1IrIl3QI5MpMC6S7/nQRmYt5OTeLyCvAh4XmRnsLsQBwLb5O0LC2XzGOrcLa6/cFJmniA9iziojcgO19piyKInIYNnTr76EPnkv2vh54OdP7qu5ePwR+ly8WkUuR2ZOOhrnVWCOLRXQIZEY/9M5y/joWBHxOC2hCpLcQC4OF2Dd/Y7zCe1VtEZGJmJX0bVf2NjXPIpWlWDQ13f2m6ZhVNAqLeEIKs5ZTxdVah6zETFujCeG2VT52P6HUo5BAHgpUOQsyVEmzKmiBVNWlIvJX7N/mElcOOCVfvjRi4S3EAsE1NG1T1VeTOKcOOBPbj5yUL+VXIjIYODURizeBa+0OnI8FWLaKyGXATFWdHefUQBCRC4FZsSLe+YQTyCF0JIpXYBZkSCBXBymQzmM5HssHfRX7W+Wt6HhBLBDEZjJfAPxPMm8o59YdjL0p3wTeyfUbUkTGAn1U9bmArncG5p7NwsTxj9myiEXkVGCDqr6djfsFjfvSHBL2U06Hi70Q24tN+/0iNgf7dPe/z2VhfzclvCAWCE7YbsDeTElHkUWkD9ZAVrFIdFPAS0xmLecCC1Q1kJGqzgq5CQtyfKyq04K4boL3PhxoDErcc42I9KKzQJbRsf+4EFibqkC69/AY7Mv5E/JwxrgXxALCJQLXq2pK84RdesQRwFGY+/JBLqxFVwP8SJClXyJyDDb+9OJsVk64yP4hqvpgtu6ZTUSkN51d7GI6C+S6ZN9DLvn8eKyoYAq2xZEXQuSDKoXFR8D1Yl2Nk06pcekRb4u15j8H2E9EntYUx3GmgvswVBOj/jdFQtHUkdjArGyR9dSbbOKqfGa5n5BAhiLY44EiEVlEh0jGFUhnFT4n1og21Kn7uUQyIkQoxroMtagSeDqRF8QCQlXXu2ak++Ly0FK8zioXBRyPCewLZK+DyUACTh52LvMo4A7gmyLyicvXywbNQG8RkXyxcjKJE8iZwEznAocL5DEAEQLZ5RRHVV0uIvcCBwIXuXzbVyP/7UQow8oEryGsikuEWcBfgFdUCaRCy7vMBYaIjAGGq+ojAV1vIGYtrsL2JzMqJCJyNFARcP3vMUAvVX3aBTnKVPXpoK6fwP3/HRvnkDVLOx9xAllPh0AOwcRrUeinq71rV211HGbh/wvbzmkX4QDgXqLU+QO1WKP5JuAK1dSNhBBF6V7Ak3XmAkOdVZQ2zk25G+ugc4OI7BvEdWOQSIfshHE5jYcBoUDKv4B9XKuqbNFMN3abE0WNdao6Q1WfAH4H3I+VFg7Dxp7+m4icLSKjRaS3iNwsItOB9ViGwAPA14CrRf5xHPAY/D97gewDT4Xd7a/1MGYQVA6DI0YBE0UYEXpWRIpF5JciskxENorITOfux8S7zAWGqm4Tkc+BA7CxAUFccwfwooh8CpwtIvsDL2QoODEIeDHA643G2vSvhp1/n5ew8aV3Z6mut4mOpgseh3OV17qfGc6CbMAsx32wjuL7Y2WYC7BWbStE5D7Y4yA49kmYUQqTaqBvxJyaxla4aSV8WgFv1GHBnvtEGO/c559jY2fHYv8uB2DzyWPiLcTCZDb2LRooLp3nTszNuUFEhgZ5fZfzVkxAw91d1Hwsu44onQNswSzHbNCtAytB4SzINao6XVUnAr8FfgBMwt4X+4rI94Az4U+HQ/9W+LdecMsms93Ct/fO3ghXN8HAkFBuwv4NThCRemxE7zWq+qW775xEKmW8IBYmXwB9XG5hoKjqNpfW8xxwjoic6tzSIBiItcwPauN6P2Az1i9wJ+76zwFHu8qMTFPwM5pzgROq1WoNdj/Byg0fBpbDqMvhnkYoEThjI1AEm3rD1ljvRcXa540CWrFGJytE5DMRuSmRNXlBLEBcFcYc7B8+U/f4HIvaVmNt+3cP4LKDsC7faePcr3HA29EEVq3mewZwchD3i4O3EAPCclN1OjT2g1+Vwx8XQcU2QKGtDL7cE1Z3ZQhsBEZD8R7YWI59sQDPecDPROSkePf3gli4zAYOdMKQEVR1i9sc/xdwoYgcL9ZrMFXSbfkVzmCsDjfWrOU3gT3EmuhmEm8hBksV3NIbJqyFUS1Qtxloh4pNULEFymPtbbdDY2jf+D/de3g28AgdpYNd4gWxcFmGuQiDMn0jVf0Ysxb7A9eIyG7JXsMJd5AR5pB12GXQRK2b9gvA6WkKeTzWY92IMnmPnkQLvF4J9/SDxgPtZ2UZXDcQ7mx3AtkVRbApFGxMemvGC2KB4tzEjARXurjfJmx/513gMhE5ygU1EqUPsE3jzGBOBOmYtfxhAofPA9ZhEceM4LYwNmJumicJRKTE5SAWA8X231IEL70CH34Jr30FL66Cvq3wu0Vwi2sZ14o1lG8ViwG2CGyvBWapbpqPeQc/EpFylzVxPvBsvPV4QSxsZgMjs2WZuE3wmVje4jBsgHmigZ0g3eUjgfcSKV90XxyTgbGJ5KGlgXebU+PHWEbALcDF7r9/DJ89ATV10F9h9EooboeGVujlPILbG6D6IPjBYJhRY/99SX/svQlwIdYHci0WYPuJJtA6z1eqFDgiciXwlqrG2kvLxH0FS2s5BngNeD9W9NhVkGxU1cgUmWTvWwvciLX4SrhTiquQGRhUhU+U65+F5UNms4662+Fq3U+G2n1gxcVQVUGUmeVRqMG2LsanU8bnLcTCJ2tuczjOWnwXK6s6EOuMHMtlDCrCfAQwO4W2UW8DfTNYieMtxDQRG8d7I7ADNv4Jqi7C+lzWxDm1xh13Rbo1zV4QC5+PgWFuHybruPSWe7Ba1WtFZJfIt3Pp+5OmIIrNWj6IjjK9ZNbZCjwPnBZgXmU4PvUmRUSkVkTOx1qCTVTV5y0flrnABMzyq8Nql8OpdY+vByb4WmZPqJXSQqwEKldraFfVN7A61HHA+WLT4EL0BZoDKAU8GJivKQ6eV9UvMFE+Ks11RMNbiEkixhhsKNhqrEFGp/JHJ3LjsbGyc7HSv3r3e657fHwQYgi+lrm7MBs4HGvLlDNcHerdwLFY6d9zarNG0naXnZV5BBbpTocXsZZns1V1bZrXCsdbiEngyuvOwHJJH9AYk/mcGzwZmCzCzpnlvh+ipys+B84UkV6quj6XC3Gu6Suut905IrIf5oksjn1mXAKZtayqG0RkKpab+I8Aywg3AeUiUubyHz1RcKlah2NW31vAtGQacDgRTCTIkhLeZe4GOBGaSwZL+ZJFVRdjjSK2YcOxUv7yDSvTSytCHca72P7TiHgHJooTVu82x0BE+gFXAcOBv6rqW1nqRpQwXhC7Dx+S4VK+ZHGW0stYa/+xIvJ1ESlL4VJ7Y9m3CwJaVxuWm3aKC9QEhXebo+CSr48FLgc+AP6uqutyuqgu8ILYfVgMlGLR3HxiAPAZcBs2we16sbnMyXAkXTRxSBXX6mwBru19QHgLMQLXFOQ67H1wp2sem7fJz14QuwnZLuVLglDLr62qOglrBvotETlJROK60W7EQR8svShoXgZGp1Kb3QXeQnSISJlLxr8AS9x/RFU35HZV8fGC2L2YDYxKssY403SKMKvqp1ijiD5Y3uKAOOePA97RDAyed3XV/8K6awex1eBHCQCuu9AN2HS821X143y2CsPJpw+OJ01ckvR6INPtrpJhlxpmJ0SPAVOBi0Xk6Ggi7lIzhmL7TpliBhbwOTCAa4VGCfRIRKTSlTCehQ0sm6TZm34YCF4Qux954za7utQaosxgdqV/s4G7sCL8q0SkMeKwscCMABK6u8RFOZ8DTnTrTYcmoD6fAlvZonPZHber6vwcLyklvCB2P+ZgsylSieYGzUBgeZyehRuAf2CD0K8UkSNcBXYT7NwAABCTSURBVENo1vK7mV6kqi7FWtgfn+Z1tmLR8HSFtWDoquwu1+tKFZ+Y3c1Q1c0i8hU2b2R2jpeTUENYt7/0voh8gc2I3g+zKj9xfRizwRTgJhGZqTaaNVVCgZWCchWTxVnBo7EB8jOAJxJpx5bveAuxezKbYPbE0iWpHoguN+0+LB3mBmBTttxPVxP+CvCNNINS3T71xu3tXgIcipXdTekOYgheELsr84BBWZo4F4uka5ide70FeBobEnRhFl/Hh1gr5oPSuEa3Tb0RkSIRGQtcg01+/GusGuRCxAtiN0Rt8PynWP1vTpAUZzBLx6zlycBfgOVYMvcBgS8yAue6PwccF9GtJxm6pSBGlN3dk49ld0HgBbH78iG5jTanOoN5P2Czqn6lqm2q+i/gIUykznPBloyhqiuxLYe4Iyu7oFu5zF2U3QXZJSiv8ILYffkSqHbf7LkgaXe5qyYOLgp8F9bl5AYR2SeoRXbBa8BeIrJnCud2Gwux0MrugsALYjfFuTMfkTsrMZWRo3vSxaxlVd2hqi8AT2CVJWcG3Jgh/F7bsL6JX09hgFczUJdn1UJJEVF29zoFUnYXBAX7j+ZJiFApX1YThd39UmkKG7eJg6ouwkr/wKzFISksMRHmYqNFD0vmJBdt3cKu7e4Lgihld3O6u1UYjhfEbozbD9uCWV7ZJDSDOeEcQufaJzRr2eZt6NPYjJRzReSUoOekOBF4HhjvAkTJUHD7iN2h7C4IvCB2f3KRk5iKu5zwrOUQqvoZZi3WAdeJyKAk7xnv+muB6cApSZ5aUPuI3aXsLgi8IHZ/PgL2y9Ckua5IKiHbWWDDgfeTvZGqtqjqRCwQcpGIHJfCvl8s3gQGisiwJM4pCEHsbmV3QeAFsZujqhuxvbxMzSOORrL7h4cDH6Ywa3knqjoHG1kwELg6qOi6y+mcjM1gSbTUNa9d5kSm3fVUvCD2DLLmNrvo6m4kKIjSMWv5nXTv7cT/IczSvFxExgUR7XWu+WrMrU+EvLUQu3PZXRB4QewZfAIMTqP6Ihn6ARuScL3SmrUciWsr9gFW5bIPJox9Arj0C8ARTlDikXcWYk8ouwsCL4g9ADfs6XMg4+VvJLF/GDZrOahpejtR1Sbg79iXwdUicmg66UdOsKcBpyVwnQ1YUnxedJPqKWV3QeAFseeQrVK+ZCLMo7BZyxmxVJy1OA3roDMG686dbApNOG9jKUXD49y3HRPFnFqJPa3sLgi8IPYcFgC9RaQhw/dJKKDirKwjyYB1GImqrgbuAb7C0nO+loq16Oa6PA+cmkAD3pyOE3Bld9fSg8rugsALYg/BWS1zyKCV6FJ7GoBELL5AZy3HwzWKeB3rzn0UNvkv6T1VVV0ALAHGxzk0J4GViLK7N+hBZXdB4AWxZzEbSMk6SpD+wOoEo5bjCHjWciKo6nLgbmAdVvq3XwqXeRE4OMoMmHCyHljp6WV3QeAFsWexHGuAunuGrp+ouzwIs54yMWs5LqraqqovY5P/ThGRs0WkIonzN2LWV6zxpVmzECPK7p7vqWV3QeAFsQfhrIVM5iQmGmE+EpimGZi1nAwuGfkO7EviBmdhJcp7QBVdR+6zYiFGKbv7PNP37M54Qex5fASMCLi8LUTcCLPLCcz0rOWEUdXtqvos8AxwtoicnsjEQrcn+yxmYUZrQ5ZRC9GX3WUGL4g9DJdPtxpLWg4MsZnGtUSZwRxBaNby9iDvny6uocEdWD/G60RkjwTOWQzMB46L8nQLUJyMK54Ivuwus3hB7JlkIicx7gxm1/5/JFmYtZwKqrpFVZ8EXgXOF5ETE0iufhnrOdk/4lpKwG6zL7vLPF4QeyZzgWHOqguKRBKyDwPmZnHWckqo6lysUUQjcE2k2EUc24LNdI4WYAnEbfZld9nDC2IPRFW3Yh+sEQFeNmaE2eUoHoqVv+U9TrQfxdZ7qYiMj9Eo4gPsszQ64vG0LURXdnclvuwuK3hB7LkE7TbHsxBHA4tVNd4eY97gSv9mYQOuhgJXRqv0ce7xs8AJEVMBU7YQI8ruZuLL7rKCF8Sey3ygr4ikvcclNki+hC5mMDvLKitleplAVdcDD2ApS1eJyOGR7rFL+J4LnBD2cEoWoi+7yx1eEHsoLgfwY4KxEgcBy2J8aPcHNrmobEHirMX3sJroUZgbHSl2U4B9naABNJVDH0RqSKAvoy+7yz1eEHs2QZXydekuZ7OJQzZwbuu92B7stSIyJvT3c3uzL9fBmTtEvt4Kdy+H/1TbnvgCkUmInE6UPEdfdpcf5EW/Nk/OWIJ9KQ4g+ZGh4Qyi61SaLmctFyouqDH1/2/v3mOrrs84jr+fXmjpjRYdSJGblutwUcy8bSxmOplmJpvRuCwuyjIXE3WXaMyW6W6azWW6mCzLjMniJTMu0THItripsHhhGQmZjiEWBYHJQEBoS0uv9Dz74/keeiinpUDv/bwSAj38CucXwiff83u+3+cxs/eAG4iZNX9y95ZO6D4I93RBURm0t8KRSmgqikYWS4DHgAbMVuK+JVX6rwHOA/6skyYjSyvECSznKN9pf2xOq6Na+g7UEWniMBTM7C4z22hmHWb2lMeY1ycAA5oLzdqqYdP5MO+7UH0UjhRC9x1w7hxYWg5182DW4zALeP4XZtcTx+66iU7jr5pZs5m9ORjPduXUaYUo2ULBS6e5naMG6My3tzBtGZlBbF8ZD/YADxFjSSdDPIs1s38AbId9NVBUAfsOQ2UjVBVBdxmwGrZ9AtpfhfIvwvxZUPwV+NXTcNXbsJIYtHU50bPx40D7iNzhBKcV4gTn7oeI7SGnMmYzV38NHa4ANoyX0xTuvsrdVwN5t7/UQmc3tO6DaZOgsxMmZcAehEMXQXsBcAlklkHXevBa6Ho6Bmx9G7jd3Xel4s3m9DxShpkCUeDM9iTm3ZBtPbOWN57B+xpTZsO8xTD3bijfBtUG3gplXVDUBYUH4Kz9UPE2FC2DRoPMLrib6LZzo5l9aGbvmtmdI30vE5UCUSC238zvo2vLyfRVYT7jWctjxXlwcD3s+QD+vRG2HAHuhMpJ0NUBJQ0wdT+cXQLt90L5Imi9IWauNDfCImAKMTd7HnAj8CMz+9wI3tKEpUCU7HncXcR+wQFLG67PIRrP5r5eyiDNWh4LtoNfAe3FwCw4+jjsXg9VDVBQDF2l0DYNProParbC5DWwPfsfrzSqzwA/Sc0lNgG/B64bkZuZ4FRUkaxNxIzkt07he7IzmHs/7xrUWctjQGs3FB2B8jYoPQglACXQUQsNheDfgdp1MOV1qJ/aE4Isi8auAGO+Cj8eaIUoWVuBGac4pvOEj8up8eyljJON2LnS+eJSoJDodTjXzK4y+Nka6OiGyjZoewBKL4HmWbHtxr8H56yCqa/Au+fEFpusykXxjPV14PtmVmJmi4GbibPRMsy0QhQg5oyY2TvEsbSBhlm+CvMFxKCp8die6gHgBzlf30JM8dvwVahymFYO0z4Nh5/PmSb4MMwsBl8cvSAB+CbsfTiayD5BrM5/S1Sv9wMPuPva4bghOZ6Ng/2yMkjMbC5wrbv/ZoDX30Gcrtidvjbi+Nlf07jOMS+NEzifKH7MJxo21KcfB45tOI/rXicKJAPp91gBNAHLGWXdwycyrRAl1y6g1Mymp1MYfepjBvN84vnYjqF7i0MvzWteQITgXOKIYz2wts9mC+6dmK0EnifCrr9QrCA+Oq9UGI4uCkQ5xt3dzLJH+V4+yeX5ZjBfAawfi8f00vCrhUQITieaN2wG/jjgTdLuWzC7CXiSOMHjQHPOFZXEMb8GIgy3DNoNyKBQIEpvm4jWVmtPcpTvuA3ZadZyNdETcNRLH+9nEAG4iBgpuhV4A9hx2qdrIhSXE30Rv0E0xs0QBcy3iGeGa7UyHJ0UiHIcdz9gZi3ER8X+ngPWcvxH408B/xzpWcv9SRXwOUQALiROiNQTI0h3D9rKNsLuReDF1AexDGhFrf9HPQWi5JM9ytdfIM4kVlPZj5tzgdVD/s5OUSqK1NFTFDlEhODvgI+G/ON9hOCoHqolPRSIks9m4EozK3b3rt6/mfbi5c5gvhzYOFpmLZtZBT1FkTnAB0QIvuzuzf19r0xsCkQ5gbu3mNluIlD+k+eSYzOYU0V2KfDr4XyPvaXhT9miyDRiZswmYJU6x8hAKRClL9lqc75AzN2Q/UlGYNZyTmPabFFkMrEKfA3YOV5ajsnwUiBKX+qB68ysIk/YzQQ258xafnI43lAqisylpyjSmd7nGuB/Y3G7j4wuCkTJy907zWwr0b2597yUWuBvwEUM8azl1JIsWxSpI4631QPPjKUZzzI2KBClP5uI/XTHAjFnBnMTUUxZNdh/aSqKZJ8Hziba6tcDL6koIkNJgSj92QFUmtnZOaux7IbsxUDzYM1aTkWR7PPAjwHvERuZX3D3jsH4O0RORs0dpF9mdg1w1N3XmVEIi1fAjnboqANec/f60/xzjQjX7EqwlJ6mCTtH8wZvGb+0QpSTuPgdWHG/md8NdiFsKIOiDOzcDwt3m/G+OwPaf5iKIvPoKYq0EwG4GtijooiMNK0QJygzuwu4jehf+Jy735Zevwx4ELg4+qBe7fBIBhYchuIGWL4U/jUpehRAFHqLtrm3LTCz2Zx4lrkceIR4DlkHHCCtBN097/Q6kZGiFeLEdcKM4aQGeAJe2QmXPg1fr4U7SmBNI1QVwnMHoSADM/ZFv4LLlsBnqs1Y4tG9pSIVXhYCy4FHiZMiO4g+iTrGJqOWVogTnJk9BJybXSHGa+Q0O30jAysWwta9UN0EH50FNY0wpQW2ToIlF8CW92FeI8y+B/bVEX0S3wM+Cyx19ytH4NZETplmqkg+VxMrxRZYVwF1bVDcBc2VkCmAiiPR6u/xabCsDaqKoHk23L8cWAc84u6rgGuBp0buNkROjQJR8rkdcNgwGR6thZ/vhvJWOFwFJR3QWAV7psMLZ8HNTTC1EaYegruWufv77t5t0RNwOvDCCN+LyIDpGaIcx4wC4ELY3ALXL4Sf/hc+3wIZA/P4UXwUNrTBwQK4fS+UZIhxmheaUeBOBrgV+IOeGcpYokCU3spgWwGsWAD37oU7D8XLBQ7zt/dUl5+ZAysaYEpu09MMUGZm3cBNwJeG9Z2LnCEF4gRlZkXEv392xnApcBSmVMOUWvjah3DfgV7flX5uMfhLDTy7vdcfW0CM1vwyMZ3u70N5DyKDTYE4cd0P/DDn61uAH0OTQ1MR/HJmPD/Man2z59fP1kBlN3yh9wClt9zJmHEr0XxBWxhkTNG2GzmBGdcBjwH5R27mVwV8y50Xh+ZdiQw9VZkln1eIUZkVA7y+Il2/dsjekcgwUCDKCdLZ5JXEMPWTheKxoesDPdMsMlopECUvd7YQleIm4uNwZa9LKtPrTcBN6XqRMU3PEKVf6Rhfv0PXtTKU8UKBKAOWNm2XAa1p87XIuKJAFBFJ9AxRRCRRIIqIJApEEZFEgSgikigQRUQSBaKISKJAFBFJFIgiIokCUUQkUSCKiCQKRBGRRIEoIpIoEEVEEgWiiEiiQBQRSRSIIiKJAlFEJFEgiogkCkQRkUSBKCKSKBBFRBIFoohIokAUEUkUiCIiiQJRRCRRIIqIJApEEZFEgSgikigQRUQSBaKISKJAFBFJFIgiIsn/ASgIIlrn7NSoAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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50ZHA8djM9peqWpfwMzGsyHsWdgQwWeecnhoK/COF79clHo7OZYeMnKXuRBVwcPwXwmbLFGwJvRm4LVlvSbHrUC/ELr+6OQ1lSD5zdK4vCh1xxgMPRjiM3ZbVIjIaOB0oAR5R1aQzt9BZ5yLshr8nNcXnncMOfjkW3hnl4ehc9A4CPuhu/V+KVQMDRGQg1jFnHPAUsDxZ4IVZ5THAccBDqroyTeMaAmxLdeh2hYejc9Gbjs28ohQDxhTBlw6EF0bAL55SbUr2g2Gmex7WT/GWNDfIiGRJDR6OzkUq7AAfANwb0e+PjYYjvgZXnQ8fPxRKSuBKIIbIcuAWYElHv0QRGYX1XlyJ7Va37f3dUyKSMh7wcHQuagcD7/fkAqjeEpEDL4R5v4BLhwD10K8FqkqsOzjYNQ0/Bba3iMwvtpMqJwN/UNVMbR4NBd7J0O/ajV+T4Fy00lL4Ha4lXSAiq0WkRkSWicgZ4XujReSFInjpPvjGMigqgu0Kta1QsAUKLoBxg2HCYBj/VZhYB49fYMcAFwB/EJEGEakN/3ki1eOPk/FWZR185uhcREIJzCjg3TS8fSHwIVa0vQY4E7hHRL4IDC+C5x6C/vOgvC3MFAugrRmKPw/7N0BsNby+GvqdAZNGQ+xeOCMG3w9XBp6jqkvSMO6dQu3kYOza1YzzmaNz0ZkKvNvFZq/doqp1qvptVV2F/Tmvwjpojwd+1gyPnwFFAjt3gQuhtRUKlsLAr8EGgZJKqPg0bLsTimJ2vPCUVI+1EwOB+igeOYCHo3NRSutZ6oRrT6didYyLwimcq4DdjvYVQlubFXJTA+U1UDEMtsag5V0oDT9/dfjxRSKyWUSeEJFD0/QRItupBg9H5yIhIhXAcOD9NL1//LWni7F+ineo6tvYcnUmsNtJlkJoa4Gi46HppzC4BLauhIK7YWijZUUNMLMYLsfqIMditZCPi0g67r72cHSuD5oGvJPYuKG3RKRSROZip1ZeAG4FvoddaHVd+LEy4pbTAA1QsgUq66H/j2FjGTRNhunnwYHnw7YR9nqA9iYrDG9Q1XpV/W9syX5CKj9HEGk4+oaMc9GYhjWATYlQmH0iu649fRDrs/hrrLXYmXHPNuuBWLP9+ZcaqKwOjWTLobYUeBh2No64DkbP3NXnMcaeTWcVkFR9ljjDiK6Fm88cncu0cERvCCnoNCMiBSJyJPAFoB/wK1X9awjCG7HGEed0dPsRkVKBw1+F6o22U04h1JTDthYoGA6bV0DpWihuBe6BAYtg6LfsTuuKFfCOwDEiUiwi/UTkq9gM79nefpYkfOboXB8zDXirN6dLwtnmSVgn7h3AnfGXVonIWOAarOHshvDzMeAh4L5jYEyDBTSfCjcPPg9r9oeWN4ALYWotyFhouhU+mA2NQPGf4QEsdCdiX1sOnKGqKS23CSeHYmTojuqkY8hw53Hn+jwRuRpYsrdON114/UisY04Fdt/Me8mayob7oWcCM7AAXQ68oaoNWHPdp4GB7VC3HoYPg63F0NoGsfUwfCRsKtz1bLIca05xAhkorQkbSqep6q3p/l174zNH5zJIRAYDA4BVPXhtBXZ8bxJ27ekribNPESnFSoRmht/zGnYV6u6nTFSbEZkP3NsAQ0ugudieUVIA7WXQUAv9B9kOdTnQBszPRDAGkS6pwcPRuUzrWFJ3uQVXuELhGOBo4BXirj0N349h90QfGv76LlZi849Of4/qilUilxbAI/vZVyoI5T0VUFsNo9shFoNtWDCu6M4H7SUPR+f6mOnAo135wSTXnt6sqtvjvj+cXcvmKmzZvLg7Vy2MhwGV8NVttuy+OrxfexHEdsAHj8I9V8L/ZHDG2GEo9i+CyHg4Opch4da+Mizo9vWz47Dnim1Ya7APw9fL2LVsrgBeBW5X1W7PskSkBDh6O9yGvf6xUCBeBtRPtCL1y+ZBewQ7Ez5zdC7v2R3OpSVwSBO82dmNfCIyBLuzZSSwBLtXJiYik7FAnIj1UlyKdQ/vTYfso7B2abtCyN6vFkBtl3sjNjPN2CwuXOg1ALu6ITIejs6lgz0nnIOdYZ6p0L4RBsXgxTA7WxK/VE249vRvwO+xUpvTwte2Y8vmh1NxnUIoGj8aa0HWmWeAc0Qk6XUJaTIEqMpAI91OeTg610VhGforLPQGA+8BX1fVx8Kmyd3AbGDsI/DW2fbnS4GtG6Dk8zDiGXvtnCthw09EThNr5Hok8F1sM2UMcBu2cdOfXiyb9+EorCPQvuoTV2MtzQ4GMrUhE1kPx3gejs513d56JB4CrAOe+TQ8uBRuK7Dyl00dL7wWDmgEXQWvrYPCU+HgcfDUuXDrQ/AWNlt8ETgXW1IuoffL5qTCrPEo9j1rRFVVRJ4FjheRtzp7JJBCkT9vBD8+6FyXxfdIVNV2VV2MnUGeparNCr/6DXwhBrTtumoABZ6E8q/C+gpoHwd6EdTeBZX/C58ut9niKuwemeVYqc/7aVzGHg2s7MaplrexK1rHpWk8iTwcnctlIjICmIxtmoAtmSs1oU9iMxQBCOhmGLwORrZD0TtQWAElL1g94q9V9RUSuuWkYcz9sGV8l5tehNnis8Dx6RpXAg9H53JVuGx+ER09Es0eDWQB6qDseGj+Lxj3EQxYB433QXEj0B/qpsAlGRz60VirtG3dfN3rwDAR2S8NY9op1HZ6ODqXi8KJlDuJ75G4lwayLVCwEYZ/A1rKoGkODJwHw8+HraFHYg0wM7w+3eMuxWaNT3f3taHv5N+B41I9rgQDgUbdy53ZmeTh6Fw3hJnNAqxH4oVxPRL3aCDbCrHNMKQfNE6ArTdB9SpY+S682Q4S1yOxPbw+3Xo6a+zwMjAhnA9Pl6yYNYKHo3PdtUePxKC+EWL1oelrI8TWwNAyqCuBpg1Q3wLVVdD/Dth/EQwLPRIBYp+A5vA8MAYUhl6JBakadJg1HkEvGuyG2dxLwLGpGlcSWROO3rLMuS4KPRJXYT0S4683uEZVF40QqduUMAN8G16vgEGLoe0bMHoHFIyDlq9BzTlQNQi0AN4Uawc2L+FXzlfV21M09pOBclV9uJfv0x97lPBLVU15r0URORvYpKovpPq9uz0WD0fnUkTkzHb42SYoKoGmQVAjwLrQK7HIzkkD0AZSDRUKlX+E/7ocfp6uEyHh9M0XgJtUtSoF73cW9lxwaa8Ht+d7fwb4a097XaaSL6udS5HvwF82QkEZFHQEI+y8XGW3O1YKQAdDewWsudaOBn5eRCamaWjHACtSEYzB34BZ4cRQqmXNstpPyDiXAqG0Z+4a+PEt8C9iJ2Q6lp3J1mflQFsxXFFtJ2QOAs4OjR4ej29N1stxlWFHGm9KxfsBqOp2EfkHMAsLypQIz0WLSdjxj4rPHJ3rpdBF5mJgxwK4UWAu9gxxANZWLF5F+Ho1MBfVFWreBn4JfARcLSKnhPPavXUs1gkoVbPGDs9gF22lcoI1BNiSoSOK++Th6FwvhB3li7CaxQdVtT10zD4B+CKwogzKYzAI+8O/Inz9hMTO2qraqqpPYzviA4HrRGRGKB/qydj6Y7O7btc17ku4zKujnVmqDCNLltTgGzLO9VgoBr8AO3f8271tqBSJXPdpWHwnrKF71yMcAJwBtACPqer6fbwk8fVzgBJV/UN3XteN9x8PnIVdB9vrY48icirQpKopu8+7N3zm6FwPhNncJ7HSnd91ttPcCu13QUN3ghFAVdcAt2Btyy4TkXPCbLAr4+uYNT7Tnd/ZTauwsqaDUvR+WdGqrIOHo3PdFILxTKyn42/D0bq0CN1/XgZ+gc0grxWRo7tQIH4sdg1rdRrHplj4Ht/TpX+CrNmpBg9H57olhMCpwChgkXbt4ikloZSnu1S1UVX/iDXCnUwnpT9h1ng4aXjWmERK2pmFsB9IxFcjxPNwdK57Pobd43JXN5ojpOzBfrh/+k7sDpmzReTTIlKZ8GPHAa+r6o5U/d5OxqNYOU9vG1IMBqrTOQvvLg9H57pIRI7Hri9Y2J3rTztenqpx7KX052QRKRaRcuAw0vusMdFrwHARGdmL98iqJTV4ODrXJSJyFLZUXaiqdfv6+QS9XlYnfdPdS38qsTPPlwGvZWLWGD8OrJ1Zb5rhejg6l2tE5HBsg2NhJkOnq1R1h6reBzyK3XU9Pt1NaZPoaGeWuMTvqqyqcQQPR+c6JSIzsOeMC3txyiQtM8ckxmGlP8/TzdKf3grPX1+m5+3MfOboXK4QkanYvdF3duMyqkiISAVwKPBMKP35JbtKf45KZW/ITjwPTA/PPbssm65GiOfh6FwSIjIZO/2xKOwQ90YmZo7HA8tVtQZAVRtC6c/tWJH250VkQjoHEPo7voFd+9odFUBzDza50srD0bkEIUTOBX7T3SN7UQizxhnYDYG7UdVN7Cr9OUdELu7Fc8Gu6Ek7s6ybNYKHo3O7CeeZLwLuUdW1KXrbdM8cO2aNSTtzJ5T+rCeu9CfVAwmt1jramXWVh6Nz2UxERmOtx+5T1dUpfOu0haOIDGAvs8Y9BmGlP38lrvRHRKan6OhfvGeBo7vRzszD0blsFQqYLwUeVtX3ox5PNxwPLOvOfS5xpT/3hdd/JpWlP+FRxGbgkC6+xMPRuWwkIsOAy4FHVfWdNPyKtMwcRWQgFkD7nDUmE2bHN2MnXC4XkbND5/BUeAY4rouz0qyrcQQPR9fHhTuYrwD+pKpvRj2ebjoeeKUHJ3Z2Suj608au0p/eZsMqrJ3ZwZ39UNi46Yd1Rs8qHo6uzwozryux2+5eTeOvSvnMMYx9Oim6wyWU/jwG3EEKSn9CQ4pn2Xc7s6Fk0dUI8TwcXZ8Uyl/mAX9X1ZeiHk8PnAC83JtZYzJxpT9PAZ8MpT+Devh2b2OzwrGd/ExWPm8ED0fXB4UjdVdiGxl/z8CvTOnMMYTVNFJ481+8UPrzFrtKf64RkY93t/QnXJ3wLJ03pPBwdC4bhOs/rwDeCh1tctEJwEuqWp/OX6KqLaH053+xy8Gu7UHpz2vAiE7amXk4Ohe18PD/cuADbNmYKSmbOYZZ41TguVS8X1eoarWq/h64n12lP13q3RjXzmxvzXA9HJ2LkogUYXWM64EnMrwBkMpldUZmjcnElf68DlzRjdKfl4CJiccWQzOMSiArm3p4OLq8F05qfBqoAv6QjTujXRHCZQppetbYFaH05yV2L/05srPSn07amVUCNdl0NUI8D0eX18Ls5FNAI/BQRMGYqpljx6wx8u41CaU/U7DSn/GdvKSjnZn1lxQpOAEOKMrSJTVAV88+OpdzwmzmAiyc7k/FxfNRCbPGg4H/iXos8VR1k4gsxMZ2roiswx5bVCX8XO1QkXdugC9gV07MfByKFQoQuQhr0ruErt3mmBGSoysM5zoVdlTPA8qx1mORLd1E5HLgeVV9txfvcS6wQ1UzuZHULeG57rFYP8cXsca7LeGb01pg4Q44oBK2xaBmKwwqhuYKKMBm1tuB+aiuiOozxPNltcs7IRjPBgYBv83WZ1pdFY44HoTt+mYdESkRkQXAe8Bi7JKvOVjXn5lDRB4fA8uK4fCl0FwL7QAtUNgKbZdC5RAYPwhmz4Hnfynysbj3niIiT4pItYi8JyLnZ+pzeTi6vBKC8XRgBHD3zplLtHr7zPFE4IVseNa4F4XAh8BJwEDgP4DrgRcq4MRrYNYC2DgUWkqgoRbKFWiFwh/B4JehfDm8uQ6WD4T2B+F+7JrZQuAhLHAHA1cDd4Uu7Wnn4ejyzcnYcbW7wi5pNujxs6swa5xMls4aAVS1TlW/raqrwm72YqyWdORWeP+bUDcdiIHEoL0QWmqgv4CugqKPw479obUMdC5set8ehZyCPcccBfxEVdtU9UnsxM0VmfhcHo4ub4jIidgfqDtVtTHq8STo6czxJOx5ZbZ9nr0SkRFYoL9ZBJ8rhcaRsAmgBgYVQHs1DCiE1mtgywtQvgqKaiC2CAbPgVpslpjsn5lgDTfSzsPR5QUROQaYiV2hmvEC6X3o0bJaRIYAk7AymJwQNmUWAXcorMT+N6kpsH8G2h92tEJBLQxoh4Lp0DgamsbDjEo47D0o/S6sBmaeDu9gofpVESkSkdOwf1mkqudkpzwcXc4TkdnYDukdHbfv5Ym+s3gBAAATR0lEQVQTyaFZYyiduhNoBq7DQmy38qlWKG6DgnLYMQy2fAbGNkJsAyyvgVfOhu2n2r8Q2v8IxVjFwVnABuD/APcAqbrbp1Meji6nichMLEQWqmrWNUwNuj1zFJGhWEhk7bPGeGEjbAG2EXZh2AirV4g1QvEWOw0Ta4eCIbB9f1hfCO1vQdk82DoC2kpB/w02vQ79N9omT72qvqaqJ6nqEFU9HZgAvJCJz+Th6HKWiEzDHtwvVNVtUY8nxU7Eek1my6bSvtyInZQ5R1UbRKSfwBFvw46tMLwNWoD2Aqhrg9aO6eShUHcnDNkKBU0gP4JhI6B1BLyCaruIzBCRfiJSJiJfAfbD7uJOOw9Hl5NE5CDgDGxXOmuPoAXdmjmGWeNEcuRZo4iMBa7Bni9uFJEG7NqDS7fCT46CISPhoE1QdCFM6g+Hv2tLZn4BH5ZA+ySYPhQO/RMMvNeag9wc3v4K7O83Yf8iPDVT/8LwEzIu54jIROxY4CJVXRf1ePZFRC4GXtcunvwQkQuBTbnSbzJswkwHZmNlOC/RcSOiNch9Gqt/7MoNieVYsJ4Q9VFCP1vtcoqIjAMuxE6+ZH0wBl2eOYabECdghc9ZLcxwZ2P3Zq8F/gK8t9sZdtVmROYD92LB11lAlmOdfuZHHYzg4ehyiIiMAeYC96rqmqjH0w3dWVafBDyXrc8aQ5ejg7FQHAYsA25ObDSxG9UViMwFbsM2ZhSIryqoIAvPVns4upwQLp2/BHhQVT+IejzpICLDgfHAw1GPJVG47XAWcDjWZuwl7KqJti69gQXkCdhzw6ux55Pt2L7HcuwZ49JsmDF28HB0WS+ExmXA4t50tolQV2eOJwF/0ywJiFC3OBGbJR6A3Qdzh6pu7tEb2ud6DHgMe+8yoJ4sbSXn4eiyWjglcgXweLgRLy+FfwGMxRotRD2W/sBhWCjWY7PE+1Ia2haIXdmgiYyHo8ta4TKpK4GnVPX1qMfTC12ZOX6MCGeNoYj7ACwQJwFvYc92P4piPNnAw9FlJREZAMzDAuOVqMeTTqFRwwHAgxH87n7YbvNs7PnfS8CjWdweLWM8HF3WEZFybMb4kqrmRCH0Puxr5pjxZ41hg+sI7JrX94FHgdW5evlYOng4uqwiIqXYM8Y3VPXZqMeTbuH+5wOABzLwu4qAaVgodhRr/0JVs/rZX1Q8HF3WCEu8K7B2+3+JeDip1NnM8STg2XR2LE8o1v6IZMXabg8eji4riB0zuww7abEkz5Z3ScMxzBrHAPen+heGYu2DsFli14q13W48HF3kwnLvEqy4+LE8C8bOfIwUzxrjirUPA7bS3WJtt5OHo4tUuETpU1jN2yN5Gox7zBzDhsho4L7evnkowzmQ3Yu1F/a4WNsBHo4uQuEExoVAK3YssC89A/sY8fc690BcsfYsoIF0FGv3YR6OLhIhGM/H/j/4uzxf9u02cxSRUVjT1nu7+0Z7Kdb+fV8u1k4XD0eXceEP+NlYOcndqtoa8ZDSrDQGU0pFiKnSzq5ZY5c/txdrZ56Ho8uoEIxnYDuod6azhCVKIhQDc4CrYPOxUNACtIjUvgP//iGM71JdY3g2ORurT/Ri7QzyTuAuY0IwzsHaci3MlVv1ukuEacCv2dm7cFsMilqgoh6qRkFxC5RtAOarskfvwrhi7dlYr8OXgVe8WDuz/A4Zl0knYc/J7srVYBSREhFZICKrRaRGRJaJyBnhe8UiQx6HMctAjoTFCU1d15XAvIEwZhQMmQVf+bMIU+Pee6aIvArUYTPEFuBnqvpXD8bM83B0GSEix2H3jCxU1fqox9MLhcCHWNAPBL4J3GPXN3yzCK4/GG5fD0MTHhcocO04aGqD1a/D31bAvYPgJ4+IjD9UROZhjSdWYq3LvgD8DBiSoc/lEng4urQTkSOxJeLCXJ8BqWqdqn5bVVeparuqLgY+AGbBd06CbzXBnM17/tFqLYKnyuDf1kJFO0xsg7nVcPf+8Nl5WAH8fsBnVXW9qt4HvI6VOrkIeDi6tBKRw4DjsGDcEfV4Ui20G5sMvAlchU0Rk6grA1FoKYbNg2HDMGgXWFkA3xyPXVX6D1WNv1vlVezZo4uAh6NLGxE5BDgZC8btUY8n1cLGySLgDtCV2L0oNbv/lAJNxdBYCsc1wQ/3g6Zm2F4F95ZDg9jrCiqwK0njVWMbMi4CHo4uLURkCnA6Vq6zNerxpFooYr8TaAauA8pAFZqKoKYMEKgdAB+NtNlieS3c+AGUNcLMiXD+RDh/G4xoBtrDM8oBCb9mAHuErcsUr3N0KScik7Ai77tUdVPU40m1UJJ0BzAO+DpwLhSNhE2V0FhgZTsAJfWwXzUUxB2LfDju5sTrRsPMOiAGNa8AE0SkIm5pfShwd9o/kEvKw9GllIiMB84DfqOq66MeT2+F1l/DgBHAyPDXfwZGAd8DioB3ofUZGDgH+k0FrQEUtA2aFPphi7Q3S2BIKwxtg/sHwKKhsHQtsFy17h0RWQ58S0S+gRXKz8A3ZCLjReAuZUTkAOBi7GKmVREPp9tCI4f4EByJldJsBzYCG4AC4M9AE9Ywo8M1oNthzEPwUcKk4+3X4aBmuLUSvr4/1BTA2Cb4/tqQfV9U5TErB+J24ChgDXCtqi5J08d1++Dh6FIiNFO4DHhAVd+LejydCc8Lh7B7CI7AZoEdIdjx181dPeIYjgw+jdU/dqVkqRzbdDlBFe+kk2U8HF2vhXKWK7B+jO9EPZ54oWFDYggOwzY64kNwI1Dd2zPL4cTLvdgMs7OALAfagLnJjhC66Hk4ul4J95PMAx5X1TciHIcAg9lzWVyKBV98CG5MZ8/DEJC3sfNs9W47zhVY+7Lt7OVstcsOHo6uc7YhUQrUk9CMVkQGA58BnlTV5ZkbkpQAw9k9BIcD9ey5LN4eRQebsMQ+Bbgaq39sx3ZllgM3A0t9KZ3dPBzdnuyyq9Bua48/2LcAS8QCcz52B8qL6RmGCPb8LnFZXAFsJmFZnK3NLESIAWVAfejn6HKAh6PbnUhCu609l4StUD0XnngQFqvqc6n5tVKEzf7iQ3AE1pkm8dng1j52pYKLgNc59iFhOforbFY4GLsf+uuq+piITC2DewphCsA0qPsfWDMr7vXPQNuXYP+34MBSOPwQe3b2XNz7fxH4EhZya4BzVXVlwhgEC9nEZ4MDsdvyOkLwbWBDjnfwcTnMZ459SKjj+ypWS7cGOBP4DXDIyVD3S3hiMpS2Q+0PYPhCGLoS2zBYD4XTYNo3oOpS2F4CfAANh8MRqDaLyOeA64FPY/eaTAB2YLu2ictiZc9ng1vy/B4Zl2N85tiHqGod8O24Ly0WkQ+AWUvt9rr+wI42oAD0Qyjp+MHvwYjjoOkzsL0SdghQaWd/TxGRx8P7fg0YhF2cNQKbnXYUUG8Eng1/rfU2/y7beTj2YQnttv4b0AqY2RAOA38F1gG0g7wIgw6GxlNg1GoYfyg0/hxq+sF3sZZko7Ejb6dhzRh+C3wtX++IcfnPu/L0UfHtttS6T88Eampg+TZY9l+w5nCobwdZD8M3QtEDMPBbUPcSrB8DbVfCoLEwsgj+Gt52EHYNwnHAOViZj3M5ycOxD0rebmtXickAaP8qbP48jH8NhhdAWz9oPQ2qPglrJ8Cm/wcfLIfSWmiZtOskyA9VtSqcq74Je6bpXE7ycOxjwm7xAuyZ4IVh2VtP3P8XFKiC/o0Q2wbNI2HLFKiLQXssdLqWXT8bU+tY3cxeu2A7l3s8HPueG7FynXN2Xgiv2n43fPR3GNoEsfdhyBdhdAW0HQ1VAJ+FLY/DoL9BaRPI12HUEdAwBF5ZYRs9vwP+VUQqRGQMVkC+OKLP6FyveSlPHyIiY4FVJGm3dQVMexa+sh4KS6B9BtT+ED46ynaxAbgBhv0Y9muE2GyovRW2TYBrsTrJAdixuLOwQL0F+K7vSrtc5eHoEJGCYXDKK3DLMGgtsfKbfdnZbos0NnFwLiq+rO7jRGQQ8JnNMHwTXFgCjVjwdaaj3dZ8D0aXr3zm2IeJnaM+EyvOfk5VFZEut9tC1dttubzl4dgHhRrHM7ALon6vqusSfmCf7bZ8xujynYdjHxNOxVwErAf+oKpN+3jBznZbif0cnctnHo59RKhvPAL4GNa1+9VoR+RcdvNw7ANEpAz4JNYW7PequjXiITmX9Twc81y47vMCrLnEUlVt7fQFzjnAu/LkrXB++iRgFvCQqr4b8ZCcyyk+c8xDIjIQuy2+FbtHumYfL3HOJfCZY54RkSnA2dj1Bc/68T3nesZnjnki1C6eDkwE7lPVtREPybmc5uGYB0RkOFa7uBGrXczKK0qdyyW+rM5hoXZxFnAy8ATwqi+jnUsNnznmKBEpxWoXK7HaxS0RD8m5vOLhmINCX8YLsCtQl3jtonOp58vqHBJqF0/AjgE+rKorIx6Sc3nLZ445InTavhDrkHO/1y46l14+c8wBInIwdtXp37HaRe+O41ya+cwxi4XaxVOByVjt4ocRD8m5PsPDMUuJyDCsdnEL8IjXLjqXWb6szjKhdvFwrBP3EmCZ1y46l3k+c8wiItIPe7Y4FKtd3BzxkJzrszwcs4SI7I/tRq8EnvDaReei5cvqiIXaxeOBI4HFqvp2xENyzuEzx0iF2sXzsetO71fVHREPyTkX+MwxIiIyGTsb/SLwtNcuOpddfOaYYSJSiNUuHozVLq6JeEjOuSQ8HDNIRIZitYvbsbPRDREPyTm3F76szoBQuzgTmzE+CbzstYvOZTefOaZZqF08GxiO1S5uinhIzrku8HBMIxEZg9UuvofVLrZEPCTnXBf5sjoNwjL6OOAYrHbxrYiH5JzrJp85ppiIVGC1i4XYbnR1xENyzvWAzxxTSEQmAecCLwF/9dpF53KXzxxTINQungJMBR5Q1VXRjsg511sejr0kIkOw2sVqrHaxPuIhOedSwJfVPRQ2XWYApwNPAS957aJz+cNnjj0gIiXAWcB+WO3ixoiH5JxLMQ/HbhKR0Vjt4gfAH7120bn85MvqLgrL6GPDfx5V1TcjHpJzLo185tgFIlKO1S4WY7WLVREPyTmXZj5z3AcRORCrXVwG/NlrF53rGzwc90JECrDaxelYl+4PIh6Scy6DfFmdhIgMxmoXa4CHvHbRub7HZ44JRGQG8AngL8ALXrvoXN/kM8cg1C6eCYzGahc3RDwk51yE8jocRSgASoF6Vfa6kSIio7DaxTXAY6ranKEhOueyVN4tq0UoBuYAV2FXE7QDMRGWA7cAS1Rptp8VAY7G7o1+TFXfiGbUzrlsk1czRxGmAb8GKgHFNlQ6VGD3Q28H5oOsBs7DZpb3qer2DA/XOZfFYlEPoKtEpEREFojIahGpEZFlInLGru+/fDjMexoGz4KKCTB71O7v8EwbzN4P+h8BQ1+DsQ8DG4DbgCki8kJ439dE5PiMfjjnXNbJpWV1IfAhcBL2bPBM4B4ROQR0HfznEyCF8MYbMLwVnivb9dL1hfDJSfD9D+G89dBYCRtHwdFPgwwEHgb+GbgfuAR4REQm+GzSub4rp5fVIvIa8J+wYDBc/7+w5lUYnGTj5brR8GEJ3LQDYu0wpAoKyoEvghQAN6jqtLj3XRm+tiBTn8U5l11yZlmdSERGAJOBN2HLNTCmFb46GioPhclT4fZBu376xQoYUASfGA4H7w+nToD3C4CrseeQkvj22MkY51wflZPhKCJFwCLgDtCVUDMB3imGgW2w/jX4yRr4l/HwcilsHQQbSuDBMvjZKlj7GhzQBHNHADNh+HPAKBG5RESKRGQeMBEo62QIzrk8l3PhKCIx4E6gGbgOKIPSdihUuGEd9FM4qxaOroHFA0EU+rXA6dvhpHooU/jBOljWH7YBGxuxxhJfBjZip2OWAGsj+ojOuSyQSxsyHXWJC4ARwJmq2iJCG8zcS8PZWDsMroYpg3dfOXf8d40B9ar6F+CI8DsKgfeBH6fpYzjnckCuzRxvBKYA56hqA4CdfDn5eRjdCl/fD1qAJ/rD8xVw9g572We3wOOD4G+l0CTw9VFwRAMMeUWVdhE5LCypBwA/Ataq6uMRfUbnXBbImd1qERkLrAKagNa4b10Duh2W/QrmD4V3SmFUM3zrI7gyrintDcPgx/tBYwxm18Kt22DCtao8JiK/wUqDAP4IfEFVN2XmkznnslHOhGNnwpHBp4GBQG0XXlKOXaV6QsdRQueci5dry+qkQsDNB9qw4OtMefi5+R6Mzrm9yYtwBFBlBTAXmxEOwM5Sx6sIX68G5oafd865pPJiWR0vLLFPwQq8d3blAZYDNwNLfcbonNuXvAvHeCLEsGLuTvs5OudcorwOR+ec66m8eebonHOp5OHonHNJeDg651wSHo7OOZeEh6NzziXh4eicc0l4ODrnXBIejs45l4SHo3POJeHh6JxzSXg4OudcEh6OzjmXhIejc84l4eHonHNJeDg651wSHo7OOZeEh6NzziXh4eicc0l4ODrnXBIejs45l4SHo3POJeHh6JxzSXg4OudcEh6OzjmXhIejc84l4eHonHNJeDg651wSHo7OOZeEh6NzziXh4eicc0l4ODrnXBL/HybqH9YnyAjKAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(len(subgraph_list)):\n",
    "    if subgraph_list[i].number_of_nodes() > 100 or subgraph_list[i].number_of_nodes() <= 2 :\n",
    "        pass\n",
    "    else:\n",
    "        plot_label(subgraph_list[i], partition)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Batch version"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from utils import gumbel_softmax_3d"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "bs = 128\n",
    "n = 1024\n",
    "x = torch.randn(bs, n, 1, device='cuda')*1e-5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "if torch.cuda.is_available():\n",
    "    probs = torch.empty(bs, n, 2, device='cuda')\n",
    "else:\n",
    "    probs = torch.empty(bs, n, 2)\n",
    "p = torch.sigmoid(x)\n",
    "probs[:, :, 0] = p.squeeze()\n",
    "probs[:, :, -1] = 1-probs[:, :, 0]\n",
    "logits = torch.log(probs+1e-10)\n",
    "s = gumbel_softmax_3d(logits, tau=1, hard=True)\n",
    "s = 2*s[:, :, 0]-1\n",
    "s = torch.unsqueeze(s, -1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([128, 1024, 1])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s.size()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "torch.Size([128, 1])\n"
     ]
    }
   ],
   "source": [
    "test = torch.sum(s, dim=1)\n",
    "print(test.size())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "idx = idx.reshape(-1,)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[  2.],\n",
       "        [ -8.],\n",
       "        [ -8.],\n",
       "        [-40.]], device='cuda:0')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test[idx]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(-40., dtype=float32)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test[idx].cpu().min().numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(30., device='cuda:0')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.sum(s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "s_t = torch.transpose(s, 1, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([128, 1, 1024])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "s_t.size()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = torch.randn(n, n, device='cuda')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "results = s_t @ A @ s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "torch.squeeze"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([128])"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results.squeeze_().size()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "results = results.cpu().numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "results = np.random.randint(0,2, 10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 0, 1, 0, 0, 1, 1, 1, 0])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "idx=np.argwhere(results==0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(idx)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = torch.randint(0,2,(10,))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([1, 1, 1, 0, 1, 1, 0, 1, 0, 1])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([1, 1, 1, 1, 1, 1, 1])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "constraint = constraint.numpy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "s = torch.ones(10, 100, 1)\n",
    "A = torch.ones(100, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "constraint = torch.squeeze(torch.transpose(s, 1, 2) @ A @ s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([10])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "constraint.size()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "constraint = constraint.cpu().numpy()\n",
    "# idx = np.argwhere(constraint == 0) # select constraint=0\n",
    "# print(idx.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "idx = np.argwhere(constraint == 10000) # select constraint=0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 1)"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "idx.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "cost = -1 * torch.sum(s, dim=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([[-100.],\n",
       "        [-100.],\n",
       "        [-100.],\n",
       "        [-100.],\n",
       "        [-100.],\n",
       "        [-100.],\n",
       "        [-100.],\n",
       "        [-100.],\n",
       "        [-100.],\n",
       "        [-100.]])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cost[idx.reshape(-1,)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "idx.reshape(-1,)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0],\n",
       "       [1],\n",
       "       [2],\n",
       "       [3],\n",
       "       [4],\n",
       "       [5],\n",
       "       [6],\n",
       "       [7],\n",
       "       [8],\n",
       "       [9]])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "idx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "s = torch.randn(1024, 100, 4)\n",
    "mod_mat = torch.randn(100,100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(39.1984)"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.trace(s.t() @ mod_mat @ s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "temp = torch.transpose(s, 1, 2) @ mod_mat @ s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "torch.Size([1024, 4, 4])"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "temp.size()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(-145.9816)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "torch.trace(temp[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "sum(): argument 'input' (position 1) must be Tensor, not list",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-54-7ec062ddb097>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msum\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mtorch\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtrace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtemp\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtemp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msize\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m: sum(): argument 'input' (position 1) must be Tensor, not list"
     ]
    }
   ],
   "source": [
    "torch.sum(torch.tensor[torch.trace(temp[i]) for i in range(temp.size()[0])])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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